Lord Kelvin, his life and work

HIS LIFE AND WORK

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LORD KELVIN

HIS LIFE AND WORK

By ALEXANDER RUSSELL ^

M.A., D.Sc, M.I.E.E.

PRINCIPAL OF FARADAT HOUSS, LONDON

LONDON: T. C. & E. C. JACK

67 LONG ACRE, W.C, AND EDINBURGH
NEW YORK: DODGE PUBLISHING CO.

BOSTON COLLEGE LIBRABX*
CHESTNUT HILL, MASS.

65187

PREFACE

In the life of a military leader the account of the pre-
parations for his campaigns, his successes and failures,
naturally hold the most prominent place. So, also, in
giving even a brief description of the hfe of a leader
of science, a relatively large amount of space must be
devoted to his work. A whole-hearted devotion to the
development of science for the material and intellectual
welfare of humanity is the keynote of Kelvin's Hfe.
The author has attempted to describe the scientific
work in simple language, but, owing to the very ad-
vanced and abstruse nature of much of Kelvin's work,
he is conscious that some of it will remain obscure to
the non-scientific reader. He will be happy, however,
if anything he has written induces the reader to make
a further study of the subject in Kelvin's original
memoirs, which are now accessible to all in his pubhshed
works.

A. R,

Faeaday House,
London, 1913,

CONTENTS

CHAP. PAGE

I. EARLY LIFE 9

n. CAMBRIDGE 17

in. PROFESSOR OF NATURAL PHILOSOPHY . . 25

IV. EARLY ELECTRICAL RESEARCHES ... 32

V. INVESTIGATIONS INTO THE RELATIONS BE-
TWEEN HEAT AND WORK ... 39

VI. SUBMARINE TELEGRAPHY AND NAVIGATION . 48

VH. WAVES AND VORTICES 56

Vm. THOMSON AND TAIT'S "NATURAL PHILO-
SOPHY " 64

IX. THE AGE OF THE EARTH AND THE COOLING

OF THE SUN 72

X. ELECTRICAL ENGINEER .... 79

XI. CONCLUSION .86

REFERENCES . . c . . . . 93

vli

LORD KELVIN

CHAPTER I

EAULY MFE

The effects of early upbringing and environment on a
man's life and work are always important. In the case
of Lord Kelvin these effects are especially apparent.
His father, James Thomson, was born at Armaghmore,
near Ballynahinch, County Down, Ireland, in 1786.
His grandfather was a small farmer, whose ancestors
came over from Scotland in covenanting times, probably
owing to persecution. Sprung from such a stock, the
Thomsons took a stern and serious view of hfe. The
disturbed condition of the country did not tend to
mollify this view. James Thomson, when twelve years
old, was an eyewitness of some of the horrors of the
Irish RebelUon of 1798. These scenes left an inefface-
able impression on his mind.

It is related of James Thomson that when still a boy
he discovered for himself the art of making a sundial.
As he was practically seK-educated before this discovery,
his natural abihty must have been of a high order. It
was not surprising, therefore, that when ho went to
school his progress was rapid and successful. When
he finished his course, he was offered, and accepted, the
post of assistant teacher. At this period his ambition
was to become a Presbyterian minister. Like aU true-
hearted young men, he was eager to raise the moral and
intellectual ideals of the people, and to ameliorate the
lot of the poor. His parents, gratified at the bent of

10 LORD KELVIN

his inclinations, encouraged him to follow them, and
so he remained as an assistant schoolmaster, thriftily
saving money to pay for his college education.

It was not until 1810, when he was twenty-four years
of age, that he was able to enter Glasgow University
as a student. In those days it was a long and trying
journey to get from County Down to Glasgow. The
smaU vessels which sailed between Belfast and Glasgow
were often delayed by storms, and in the summer-time
they were sometimes becalmed for days at a time in
the Firth of Clyde. Lord Kelvin relates how a smack,
laden with a cargo of lime, in which his father was once
saihng to Glasgow was becalmed, and was carried by
the tide no less than three times round Ailsa Craig, a
rocky islet about two miles in circumference, before
enough wind arose to enable them to proceed on their
voyage. On another occasion, when pressed for time,
he and some feUow-student passengers asked the captain
to land them on the coast of Ajrrshire, so that they might
walk to Glasgow — a distance of between thirty and forty
miles.

At Glasgow University James Thomson won prizes
in classics, mathematics, and natural philosophy. He
took the M.A. degree in 1812. Afterwards, he attended
aU the theological classes and most of the medical. At
that time this was not an uncommon practice of Scotch
students, whose thirst for knowledge was insatiable. As
the session lasted only sixi months, he was able, hke so
many others, to work in the summer, and so obtain money
to pay, either in whole or in part, the small coUege fees
and the necessary hving expenses during the winter.

His success as a mathematical teacher and the high
honours gained at the University led James Thomson
to abandon the idea of entering the ministry. In 1815
he obtained the post of Professor of Mathematics in

EARLY LIFE 11

the Royal Academical Institute at Belfast. This ap-
pointment he held until he was appointed to the Chair
of Mathematics in Glasgow University.

He was a very successful teacher. His treatise on
Arithmetic, published in 1819, is an excellent illustra-
tion of the lucidity of his teaching and his wide learning.
The examples given are chosen with the minutest care.
Each is an excellent illustration of some important
branch of practical theory. Many of the notes given
are of value to the antiquarian. Great stress is very
properly laid on all commercial applications. Admir-
able explanations are given even of such advanced
mathematical subjects as the theory of continued
fractions. The ingenious method of extracting square
roots by their use, which had then only just been dis-
covered by the French mathematicians, is clearly
described. References are freely given to eminent
mathematicians like Lacroix and Legendre. In many
respects, therefore, it is very unlike the books now in
use, and puts arithmetic on an altogether higher level.
The book ran through seventy editions in sixty years,
and has had a great influence on the methods of teach-
ing adopted in this country. In 1880 his sons, Pro-
fessor James Thomson and Sir WilHam Thomson,
edited the seventy-second edition.

When at Belfast, James Thomson also wrote treatises
on Geometry, Geography, Astronomy, and the Calculus.
They all give a clear logical development of the subject
under discussion, and contain many carefully worded
definitions. In after years his eldest son. Professor
James Thomson, showed a similar love for inventing
definitions characterised by minute accuracy of state-
ment. In 1829 the University of Glasgow conferred
on him the honorary degree of LL.D.

James Thomson married Miss Gardiner, the daughter

12 LORD KELVIN

of a Glasgow merchant, and had four sons and three
daughters. Whilst at Belfast, he lost his -wife and
youngest daughter. The blow was a severe one, but
he obtained consolation by devoting himself to the
education of his young family. When he removed to
Glasgow, his wife's sister, Mrs. Gall, kept house for
him. As a father, Professor Thomson was admirable.
Although a strict disciplinarian, he never ahenated the
affection of his children. The recollection of the high
ideals he set before them was ever an incentive both
to them and to his grandchildren to more strenuous
exertions and loftier actions.

The education of his elder children he personally
superintended with judicious care. In after years his
second son, WiUiam (Lord Kelvin), used frequently to
say that all that he learned as a boy in English,
geography, history, mathematics, and classics was
taught him, along with his brothers and sisters at home,
by their father. He used also to add that he never met
a better teacher in anything than his father was in
everjrthing. From 1832 to 1849 James Thomson was
Mathematical Professor at Glasgow. His death in
1849 from cholera was a great loss to the University.

WiUiam Thomson (Lord Kelvin) was born in BeKast
on June 26, 1824, and so was only eight years old when
his father removed to Glasgow. His elder brother,
James, was two years older. The Thomsons lived in
the official residence of the mathematical professor,
which was in the Old College in the High Street. The
surroundings, except on the site of the College Green,
were rather squahd. Old students, however, and the
famiUes of the professors look back on it with deep
affection. A railway station now stands on the site of
the Old College, no trace of which has been preserved.
It is difficult to reahse that the Molendinar stream once

EARLY LIFE 13

meandered through college groves tenanted by cooing
pigeons and cawing rooks. The removal, however, in
1871 of the college to the handsome buildings on
Gilmorehill was well advised, from the hygienic point
of view.

The thick fogs which sometimes occurred in the winter-
time in the neighbourhood of the Old College often made
it necessary to have the gas burning indoors all. day.
This and the cold east winds in the spring made climatic
conditions very unfavourable to the dehcate. The long
summer holiday, however, gave the professor and his
family a welcome opportunity for recuperating their
health. In 1834, for instance, he arranged with the
captain of the Glenalhin, a small steamer trading be-
tween Glasgow and Londonderry, to take him and his
family to Invercloy (Brodick), on the Island of Arran.
This is a mountainous and very picturesque island in
the Firth of Clyde. At that time it was very sparsely
populated. The Duke of Hamilton, who owned prac-
tically the whole island, would not allow his tenants
to enlarge their cottages so as to make them more at-
tractive to summer visitors. But he could not prevent
visitors from coming and Hving in the httle thatched-
roof cottages. The primitive arrangements and the dif-
ficulties experienced in obtaining even the necessaries
of life added much to the zest of the holiday. For
example, the only bread obtainable was brought from
Saltcoats, on the mainland, by a small sailing vessel,
which came, weather permitting, twice a week.

It can be readily understood how the children revelled
in the freedom from restraint, and how the excitement
of exploring glens and hills and visiting waterfalls kept
them constantly in the open air. The explorations
were real, for, with the exception of the curlews and the
plovers, they had the hiUs for a playground practically

14 LORD KELVIN

to themselves. Elizabeth, the eldest daughter, tells how
on one occasion she was so ill when she left Glasgow
that she had to be carried on board the steamer. And
yet, so great was the recuperative power of the air, in
a week or two she could go for long walks with her
brothers.

The encyclopaedic knowledge of Professor Thomson
naturally led him to take a great interest in the geology
of the island, which has now for three or four generations
been a place of pilgrimage for geologists from all parts
of the world. The northern part of the island is of
volcanic origin, and exceedingly precipitous. The lofty
precipices and deep ravines within easy reach of Inver-
cloy must have aroused the curiosity of the children,
and led them to ask many questions of their father. It
is easy to understand the fascination which problems
in connection with Plutonic action and the physics of
the earth's crust always had for his son William in
after years.

James even at this early age showed his bent as an
inventor and an engineer. He displayed much ability
in making a model boat, which the children, with aU
due ceremony, christened the St. Patrick. This shows
that they were proud of their Irish nationahty. Play-
ing with this boat and associating with the native sea-
faring men on the beach gave to Wilham a hfelong love
for nautical matters. The following extract from the
great treatise on Natural Philosophy, which he wTote in
conjunction with Professor Tait, proves that the ob-
servations of childhood often help the formulating of
important rules in later hfe.

" That the course of a sjmimetrical square-rigged
ship sailing in the direction of the wind with the rudder
amidships is unstable, and can only be kept by manipu-
lating the rudder to check infinitesimal deviations ; —

EARLY LIFE 15

and that a child's toy-boat, whether 'square-rigged'
or ' fore-and-aft-rigged,' cannot be got to sail permanently
before the wind by any permanent adjustment of rudder
and sails, and that (without a wind vane, or a weighted
tiller, acting on the rudder to do the part of steersman)
it always, after running a few yards before the wind,
turns round till nearly in a direction perpendicular to
the wind (either ' jibing ' first, or ' luffing ' without
jibing if it is a cutter or a schooner)."

We can almost picture James and WiUiam discussing
why the St. Patrick would not sail steadily with the
wind. In later years William's schooner yacht, the
Lalla Rookh, was well known to yachtsmen on the
Clyde and in the Solent. He took long voyages in it,
sometimes as far as Madeira, and had, as we shall see,
a reputation as an expert in navigation.

At the early age of ten years Wilham matriculated at
Glasgow University — and he and James went through
the arts classes together. The younger brother was
always first, but the elder was a good second. Their
fellow-students were astounded at William's quick per-
ception and his wide knowledge. The prizes were not
always given on examinational results. Some of them,
in accordance with an ancient custom, which, taking all
things into consideration, worked in some cases remark-
ably well, were voted by his classmates.

Some idea of the subjects of the lectures can be got
from the University calendar of that period. For ex-
ample, in order to get the highest distinction in mathe-
matics in the degree examinations, the candidate must
profess Lagrange's Theory of Functions and " The
Analytical Works of ApoUonius and the other Ancient
Geometricians." In natural philosophy the whole of
Newton's Principia and Laplace's Mecanique Celeste
must be known. The calendar makes the somewhat

16 LORD KELVIN

alarming statement that candidates must answer all
the questions set with perfect accuracy.

In 1839, when only fifteen, William gained a University
medal for an essay on the figure of the earth. He also
gained prizes in classics and logic, beating several very
formidable competitors, one of whom — John Caird —
was afterwards Principal of the University. Amongst
the many friends he made with his fellow-students w^as
Francis Sandford, son of Sir Daniel Sandford, the Pro-
fessor of Greek. Francis Sandford went to Oxford as
a Snell exhibitioner, and afterwards was well kno^\Ti as
a great educationahst. As Lord Sandford of Sandford,
he was one of Kelvin's sponsors when he entered the
House of Lords.

Lord Kelvin always looked back with pride and ad-
miration to the University of his young days. When
giving his inaugural address, as Chancellor of the Uni-
versity, in 1904, he made a spirited reply to the accusa-
tion that the Glasgow University of his young days was
only a stagnant survival of medisevahsm.

" The University of Adam Smith, James Watt, and
Thomas Reid was never stagnant." Nearly two cen-
turies ago it had a laboratory of human anatomy.
Seventy-five years ago it had the first students' chemical
laboratory, and sixty-five years ago it had the first
professorship of engineering in the British Empire.
Kelvin himself started the first physical laboratory
in this country, using a deserted wine-cellar in an old
professorial house for this purpose. This shows the
pointlessness of the accusation.

In 1840 Professor Thomson, with some of his family,
made a tour in Germany. During this tour WiUiam
read for the first time Fourier's great treatise on the
Conduction of Heat, which had been pubhshed eighteen
years previously. The many results obtained by mathe-

CAMBRIDGE IT

matioal analysis from a few fundamental principles, and
the elegance of the mathematical methods used, excited
his admiration to the highest degree. During all his
life he often talked and wrote about the transcendent
interest and perennial importance of Fourier's solutions
in all branches of physical science. Some of his most
important theoretical and practical work was done
with their help. Even in 1907, the year of his death,
h% was busy applying these solutions to investigate the
growth of a train of waves in water.

The reading of this book led him to write his first
paper, which is headed " Frankfort, July 1840, and
Glasgow, April 1841." In this paper he justifies
Fourier's method against the strictures passed on it
by Kelland in his Theory of Heat (1837). Kelland,
who was professor at Edinburgh University, says, " There
can be Httle doubt to any one who carefully examines
the subject that nearly all M. Fourier's Series in this
branch of the subject are erroneous." Thomson's
paper was sent by his father to Professor Kelland, and,
after being toned down somewhat, was published. His
second paper, also dated April 1841, discusses the
coohng of a heated sphere in space. In August of the
same year he published an important paper, showing
the equivalence of certain problems in heat and elec-
tricity. The paper was wTitten in Arran a few months
before he left with his father for Cambridge.

CHAPTER II

CAMBRIDGE

During last century the Cambridge School of Mathe-
matics attracted students from all parts of the w^orld.
A good position in the Tripos affixed the hall-mark

B

18 LORD KELVIN

to mathematical attainments. A Glasgow student —
Archibald Smith of Jordanhill — ^was Senior Wrangler
and first Smith's prizeman in 1836. It was not sur-
prising, therefore, that Professor James Thomson en-
couraged his son William to go to Cambridge. He
knew that WiUiam would do extremely weU in his
examinations, and that the possession of a brilhant
Cambridge degree would be a great help in appljdng
for a Scotch professorship. In particular, he had in
view the Professorship of Natural Philosophy at Glasgow
University, which in all probabihty would be vacant
before long, as Professor Meikleham was in precarious
health.

Before WiUiam Thomson went up to Cambridge, he
was perfectly competent to understand, and even to criti-
cise, the writings of the great mathematical physicists.
The training he had received at Glasgow, however, was
not exactly suited to quahfy him to win the senior
wranglership — the blue ribbon of the mathematical
world. The sturdy, independent character of the train-
ing given in Scotch universities of that day, and the love
they inculcated of knowledge for its own sake, made
the mental training which he had to undergo during
his undergraduate course, in order to accelerate his
pace in solving problems, some of which, although
extremely difficult, were of little, if any, practical value,
very irksome to him. They can be well described in
the words of Pope :

" Tricks to shew the stretch of human brain.
Mere curious pleasure, or ingenious pain."

Wilham Thomson entered St. Peter's College as a
freshman in 1841, five years after Archibald Smith's
Tripos. Amongst the undergraduates he soon obtained
the reputation of being the future Senior Wrangler, and

CAMBRIDGE 19

several of the dons who had noticed his original papers
in the Cambridge Mathematical Journal recognised the
advent of a mathematical physicist of superior abihty.

Thomson was popular with his fellow-undergraduates,
and made many Hfelong friends. One of these was
Hugh Blackburn of Trinity, who was fifth wrangler
in Thomson's year, and was afterwards his colleague
as Professor of Mathematics at Glasgow for many years.
Another great friend was G. G. Stokes of Pembroke,
who was Senior Wrangler just before Thomson came into
residence. He was very proud also of his acquaintance
with Archibald Smith, who encouraged him to proceed
with his original investigations.

In his second year Thomson read privately with
William Hopkins of St. Peter's College, whose reputa-
tion as a mathematical coach was only equalled in
after years by E. J. Routh of the same college. Hopkins
took his Tripos when thirty years old, and his position
of seventh wrangler represents most inadequately his
ability. He was not a mere crammer who studies the
idiosjmcrasies of the examiners for the year and makes
his students specialise in those subjects that will pay.
He did not want them merely to limit their aspirations
to mathematical honours, and strove to impart to them
a disinterested love of their studies. Thomson must
have been a pupil after Hopkins's own heart. During
his undergraduate course he wrote no less than sixteen
original papers, some of which are of great merit and
importance. We can well imagine that Thomson spent
httle time over the book -work papers, engrossed as he
was in problems of absorbing physical interest.

Thomson was careful always to keep his body in
perfect physical condition by taking the necessary
amount of exercise. Swimming and rowing were the
athletic exercises which attracted him most. With

20 LORD KELVIN

Hemming of Trinity, who was Senior Wrangler in 1844,
and became afterwards a distinguished lawyer, he went
shares in a " funny," and practised rowing assiduously.
He became an excellent oarsman, and won the Colquhoun
silver sculls — a prize open to all undergraduates. Dis-
tinction in athletics, however, was only a very secondary
ambition.

He always enjoyed an out-of-door life. Li a letter
to his sister, he says that the early mornings at Cam-
bridge remind him of the May mornings they used to
enjoy in the Isle of Arran. In the summer months
Thomson frequently went for a walk into the country
round Cambridge with one of his friends. He some-
times bathed in a pool in the upper Cam, well known to
undergraduates as Byron's Pool. It is in the middle
of a cowshp-covered meadow, and water-HUes grow near
the banks. It is a favourite spot for good swimmers
who hke to take a run on the meadow and then make
a flying plunge into the pool.

In his last undergraduate year the shadow of the com-
ing Tripos began to affect the pleasure of his existence.
He knew that he had an excellent chance of being Senior
Wrangler, but the chapter of accidents has always to
be considered, especially in such a severe competitive
examination. A bad headache or the expenditure of too
much time over a wrong problem would upset his chances.
Ejiowing his father's hopes, and desirous to do every-
thing to please him, a very natural anxiety began to
affect him. At the same time he was brimming with
ideas — soon .to give an enormous impetus to science,
but which would be of little help to him during the
examinations.

When the Tripos list was pubhshed, and Parkinson of
St. John's was declared Senior, Thomson being second,
he took his defeat philosophically. He sympathised

CAMBRIDGE 21

most keenly with the natural disappointment of his
father, who had done so much for him, but he had too
much common sense to attach much real importance to
a slight difference in the number of marks between him-
self and his rival. At the Smith's prize examination
their relative positions were reversed, Thomson being
first. The papers set in this examination were admir-
ably fair, and might stiU be set to mathematical
physicists. One of the questions in Earnshaw's paper
was to give a physical analogy between fluid motion,
attraction of bodies, and temperature. This seems to
have been suggested by one of Thomson's own papers
which had only recently been published. Other ques-
tions about elastic sohds and waves in canals must
have directly appealed to Thomson. In after years
he was fond of discussing some of these in his senior
mathematical class.

The papers set about this period in the Tripos
and Smith's prize examinations are exceptionally good.
Later on, when the various branches of science got more
speciahsed, the questions became much more lengthy,
and the element of luck entered more largely into the
competition. The later questions also are much less
interesting. Compare, for instance, Whewell's ques-
tion, "Does the attraction of the Moon affect the position
of a plumb-line ? " and the kindly hint attached that
you are to take into account the motion of the tides,
with the long questions sometimes set later in the cen-
tury, the meaning of which is not always clear. The
answer to Whewell's question is, that the plumb-line
is affected owing to the variation in the height of the
ocean, causing a small and variable dechnation of a
plumb-hne situated, for instance, on the shore. The com-
plete discussion of the problem is by no means easy, but it
gives plenty of scope to the student to show his abihty.

22 LORD KELVIN

Canon Wordsworth gives an amusing description of
the origin of the word " Tripos." In the days long
before written examinations, the senior bachelor had
to sit upon a three-legged stool before the proctors.
The three-legged stool was the only tripos at this
period. Later on the bachelor was called the tripos,
just as judges are sometimes called the " bench."
Subsequently the name was given to tripos speeches,
then to tripos verses, and finally to the tripos hsts.

In Thomson's time there was a trio of most dis-
tinguished senior wranglers in consecutive years. In
1841 there was Sir George Gabriel Stokes, who was
Thomson's immediate predecessor as President of the
Royal Society. In 1842 Arthur Cayley, a mathema-
tician of European eminence, was Senior. Thomson
half humorously used to say that he often tried to
get Cayley to study " useful " problems. In 1843 the
Senior was J. C. Adams, the discoverer of the planet
Uranus. Twenty years afterwards, Lord Rayleigh,
who, like Stokes and Thomson, became a president of
the Royal Society, was Senior.

There are many eminent men besides Thomson
who have been second wrangler. Whewell, of en-
cyclopaedic genius, Sylvester, one of the greatest of
mathematicians, and Clerk Maxwell, who wrote a mar-
vellously clever treatise on electricity, were all second
wranglers.

After his examinations were over, Hopkins presented
Thomson with a copy of an essay, written by George
Green, on the mathematical theory of electricity and
magnetism, which was pubhshed by private subscrip-
tion at Nottingham in 1828. Thomson learned from
this essay that the very important theorem in attrac-
tions which he had pubhshed in 1842 had been antici-
pated by Green. It is extraordinary how few people

CAMBRIDGE 23

at Cambridge or elsewhere seem to have been aware of
the existence of this essay, but the facts of Green's hfe
partly explain it.

The father of George Green was a miller, possessed
of private means, who lived at Sneinton, in Yorkshire.
The son was an entirely self-educated mathematician.
When thirty-five years old he published his essay, which
proves that he was thoroughly familiar with the writ-
ings of the French mathematicians, and more especially
^dth Poisson's work. In 1833 Murphy, a tutor of Caius
College, published a small treatise on Electricity, in which
he mentions Green as the originator of the term potential,
but he gives no reference to his theorem. At the age of
forty, Green, probably attracted by Murphy's reputa-
tion, entered Caius College, and graduated as fourth
wrangler in 1835. He did not mix much with
the students, and entered little into the life of the
college. He was elected to a fellowship, and died two
years afterwards. Thomson used his influence suc-
cessfully to get the importance of Green's work re-
cognised. His papers have been published by Caius
College in a volume edited by Norman Macleod Ferrers,
a Senior Wrangler, who himseK took no inconsiderable
part in advancing our electrical knowledge on the Hues
laid down by Green and Murphy.

In the early part of 1845 Thomson made the acquaint-
ance of the great Michael Faraday, and visited his
laboratory at the Royal Institution. In later years
he was very proud of his acquaintance with Faraday,
and used to show his class the piece of heavy glass by
means of which Faraday had first shown the connection
between light and electricity. This piece of glass had
been presented to him by Faraday himself, and he
treasured it as one of his choicest possessions. In the
summer he went to Paris with his friend, Hugh Black-

24 LORD KELVIN

bum, to study physics in the laboratory of the great
Regnault, who was then engaged in making his classical
determinations of the constants in the theory of heat.
The devices he used to secure accuracy and eliminate
sources of error were much appreciated by Thomson.
Some ten years later, when he started a physical labo-
ratory of his own, he found this Paris experience in-
valuable. He often gave reminiscences to the class
of Regnault's skill. He related how sceptical he and
Blackburn were at first when they saw Regnault freez-
ing mercury in a red-hot crucible. In order to effect
this, he utihsed the spheroidal state of hquid ether and
the low temperature caused by its rapid evaporation.

Dr. Meikleham, the Professor of Natural Philosophy
at Glasgow University, died in May 1846, Wilham
Thomson being, to his father's great dehght, unani-
mously appointed as his successor. A gloom, however,
was cast over the Thomson family later in the year
by the death of his younger brother, John, the resident
assistant at the Glasgow Royal Infirmary. He had
greatly distinguished himself at the medical classes at
the University, but he had not the robust physique of
William. He died of a fever contracted when in dis-
charge of his duty at the hospital. In 1849, three
years later, his father. Professor James Thomson, died
of cholera. Epidemics of this disease were by no means
infrequent at this period. Thomson's friend, Hugh
Blackburn, was elected to succeed him in the mathe-
matical chair.

PROFESSORIAL WORK 25

CHAPTER III

PROFESSOR OF NATURAL PHILOSOPHY

On the Srd of November 1846 Professor William Thomson
gave his first lecture to the natural philosophy class at
Glasgow. He had spent a considerable time preparing
it, and had written it out in full. Owing to nervous-
ness, however, he read it much too quickly, and he felt
that his first lecture had not been a success. He was
considerably depressed in consequence. Very shortly
afterwards, his enthusiasm for his subject made him
forget the trammels which his preconceived notions
about lecturing had put on his dehvery, and he de-
veloped a more natural style, which suited his genius.
Attendance at the natural philosophy lecture was
compulsory for all students who desired to take an
arts degree. The scientific knowledge of the bulk of
the class was therefore very hmited. As a professor,
he was too apt to forget this, and address his class as
if he were speaking before a learned society. The habit
also of making digressions, which sometimes so interested
and amused audiences at the London Royal Institution,
was rather trying to those students whose ambitions
were bounded by the degree examinations. But they
were all very proud of him, and felt that it was a rare
privilege to be one of his students.

He opened his class every morning by saying, with
his eyes shut, the third collect from the morning service
of the Church of England. He then began his lecture,
the students taking notes and looking with interest
at the apparatus, sometimes very elaborate, set out
for demonstrational purposes. Being often deeply

26 LORD KELVIN

absorbed in physical problems, it was sometimes hard
for him during lecture to keep his mind from straying
back to his own private difficulties. One felt that he
was looking forward to renewing the attack on the
problem when the lecture was over. In the senior
class he was more open. Sometimes he would branch
off during the lecture into the problem in w^hich he was
absorbed. After a hasty resume of it to the class, he
would write down the equations on the blackboard
and proceed to study them. The class had the thrilHng
experience of watching a great scientist attack an un-
solved problem in physics, and could see him try one
mathematical method after another in his attempts
to wrest the secret from Nature. Even those of the
students who could not follow him looked on with the
greatest interest. But physical discoveries are evolved
very slowly, and when at the next lecture he told us
the result, we could tell, judging by the progress he had
made during class, that he must have expended many
hours of hard thought on it in the interval. Some-
times he made an apparent discovery during lecture,
but he would generally find out afterwards in his fibrary
that he had been anticipated by others. On these oc-
casions he would always tell the result of his researches
for the benefit of his class.

The writer remembers that on one occasion, when
discussing the motion of gyrostats linked together, he
discovered certain algebraical theorems in connection
with determinants. He asked us all to verify them
and try to expand them, and finished the lecture in the
highest spirits. On the next occasion he gave a hst of
books in which he had found the theorem, and ended up
by saying that it was even given in Todhunter's Theory
of Equations !

Todhunter was an excellent mathematician, who was

®aiT02^' COLLEGE LIBRARY.

CHESTNUT HILL. MA8'i
PROFESSORIAL WORK 27

Senior Wrangler three years after Thomson's year. He
was the author of very numerous text-books, mainly on
mathematical subjects, which at that time were almost
universally used. Probably omng to their academic
nature, Thomson had an antipathy to them.

The author remembers that, when he was asked in
class to give the meaning of a symbolical expression
written on the board, he said with much complacency
that it was the hmiting value of the ratio of the incre-
ment of X to the increment of t when the latter incre-
ment was indefinitely diminished. As a matter of fact
he had learned this definition from Dr. Muir of the
High School — a mathematician of European reputation
— some years previously. His satisfaction, however,
was short-lived. Thomson's comment was, " That's
what Todhunter would say. Does nobody know that
it represents a velocity ? " The general definition
savoured too much of " cut-and-dried " mathematics.
He wanted a physical meaning for the expression.

Thomson was most enthusiastic about the conveni-
ence of the French metrical system. He rarely let an
opportunity pass of running down what he called the
British " no-system." The people of this country, he
would say, have for their unit of mass, the grain, the
scruple, the gunmaker's drachm, the apothecary's
drachm, the ounce troy, the ounce avoirdupois, the
pound troy, the pound avoirdupois, the stone (Imperial,
Ayrshire, Lanarkshire, Dumbartonshire), the stone
for hay, the stone for corn, the quarter (of a
hundredweight), the quarter (of corn), the hundred-
weight, the ton, and several other units. This he
contrasted with the beautiful French system. He con-
sidered it a remarkable phenomenon that the British
people, who pride themselves on their common sense,
should condemn themselves to so much unnecessary

28 LORD KELVIN

hard labour. The strong prejudices of many engineers
in favour of our system he put down as a strange pheno-
menon depending more on moral and social science
than on physical.

Even in his introductory lectures Thomson soared to
heights which made many of his class feel giddy and
helpless. He would say, for example, that all motion
is relative motion. We can calculate from astronomical
data the direction in which and the velocity with which
we are moving at any instant. We first compound the
known velocity of rotation of the Earth round its axis
with its motion round the Sun. This resultant motion
having been accurately determined, we have then to
compound it with the roughly known velocity of the
Sun in space. But even if this were accurately known,
it would not give us our absolute velocity in space.
For it is only the Sun's relative motion among the stars
that we can observe. In all human probability the
Sun, Moon, and stars are moving with inconceivably
great velocities relatively to other bodies in the universe.
Having thus unsettled the ideas of his class and awakened
their interest, he would point out how easy it is to get
the relative motion, by the simple device of impressing
upon all the moving bodies a velocity equal and opposite
to the velocity of the one about which the relative motion
is to be found.

Similarly, when he defined what a second of time is,
many of his class realised for the first time how extremely
difficult it is to give a rigorous definition. To say that
it is a definite fraction of the period of the earth's rota-
tion round its axis is only scientifically correct, provided
that you give the date. Observations made on ancient
echpses, dating as far back as 720 B.C., make it highly
probable that the period of the earth's rotation has
lengthened by about the three-hundredth part of a

PROFESSORIAL WORK 29

second. As a timekeeper, therefore, the earth is not
ideally perfect. He stated that a carefully arranged
metallic spring hermetically sealed in an exhausted
glass vessel would be a more accurate measurer of time.
Even in two thousand years tidal friction has quite an
appreciable effect on the length of the day. If we were
legislating for fifty million years ahead, we should also
have to take into account the effects produced by the
shrinking of the earth, due to its coohng.

In his lectures he made numerous references to
Thomson and Tait's Natural Philosophy. He was thus
enabled to avoid wearying the junior class by long
mathematical proofs on the board. He frequently
made use of terms employed in navigation and astro-
nomy when explaining physical principles. References
to parallax and aberration, azimuthal and precessional
motion, right ascension, fore and aft, starboard and
many other technical words and phrases made a large
demand on the general knowledge of the class. A
student once asked what he meant by the weather side
of a ship. His reply that it was the side towards the wind
made the student feel that he had asked an unintelH-
gent question. To remove this impression, he explained
how a ship carries a weather helm when it is necessary
to hold the helm on the weather side of its middle posi-
tion to keep the ship on its course. This suggested that
it would be useful to point out to the class that the natural
tendency of a body moving in a hquid is to turn its
length across the direction of its motion. This explains
why an elongated rifle bullet requires rapid rotation
about its axis to keep its point foremost.

Towards the end of the session, owing to the very
comprehensive programme that had to be got through,
the pace had to be quickened. The last day was always
an eventful one, the professor sometimes lecturing and

30 LORD KELVIN

showing experiments to those of the class who could
remain, long after the hour was up. The writer was
one of those who remained to the end — a period of over
four hours — ^in 1878. The whole of the theory of hght
had to be given in this time. Newton's spectrum was
first explained and illustrated by coloured diagrams.
Stokes's anticipation of Kirchhofi's discovery of the
method of spectrum analysis was then related. The
phenomena of fluorescence and phosphorescence were
explained, Stokes's theory being given, and Becquerel's
recent experiments described. The practical appHca-
tion of phosphorescent material to clock faces was
next shown. The students were invited to come down
and see for themselves the coloured images formed by
polarised hght passing through glass under compression,
quartz, &c. But even the most enthusiastic of us were
beginning to get fagged before the professor gave any
signs of concluding. The memory of that last lecture
is a treasured possession.

Some years afterwards, the writer attended Stokes's
lectures on the same subject. His calm, reflective style
was a great contrast to Thomson's impetuosity, and
the primitive apparatus he used, although admirably
adapted for its purpose, was very different from the
elaborate apparatus Thomson generally employed.
Both had singularly winning smiles when lecturing,
both were actuated by the same enthusiasm for science,
and the relations of both to their students were marked
with the most perfect old-world courtesy. Stokes was
a scholar and a scientific man, but Thomson was, in
addition, a man of affairs.

In the natural philosophy class a thorough knowledge
of Kepler's laws and Newton's deductions from them
was regarded as essential. Thomson used to mention
several astronomical treatises, but advised students to

PROFESSORIAL WORK 31

read Sir John Herschel's, not because it was the most
accurate or contained the latest discoveries, but because
of its Hterary charm. The first paragraph of the intro-
duction especially excited his admiration.

" In entering upon any scientific pursuit, one of the
student's first endeavours ought to be to prepare his
mind for the reception of truth, by dismissing, or at
least loosening his hold on, all such crude and hastily
adopted notions respecting the objects and relations he
is about to examine as may tend to embarrass or mis-
lead him ; and to strengthen himself, by something of
an effort and a resolve, for the unprejudiced admission
of any conclusion which shall appear to be supported
by careful observation and logical argument, even
should it prove of a nature adverse to notions he had
previously formed for himself, or taken up, without
examination on the credit of others. Such an effort is,
in fact, a commencement of that intellectual discipline
which forms one of the most important ends of all
science. It is the ' euphrasy and rue ' with which we
must ' purge our sight ' before we can receive and con-
template as they are the lineaments of truth and nature."

Sir John Herschel was another of the long list of dis-
tinguished senior wranglers. It is highly probable that
Sir Isaac Newton was first in his degree examination,
but no record of his place has survived. Thomson
regarded a knowledge of Newton's Principia and Her-
schel's Astronomy as essential to a hberai education.
It is interesting to remember that his grave in West-
minster Abbey is very near the graves of the two men
whose works he dehghted to praise.

32 LORD KELVIN

CHAPTER IV

EARLY ELECTRICAL RESEARCHES

Professor James Thomson, acting on the advice of
his colleague, WiUiam Thomson, the Professor of Chem-
istry at Glasgow University, had pointed out to his son
the importance of acquiring experimental skill so as to
quahfy himself better for a professorship of natural
philosophy. It was, in fact, with this end in view that
he went to Regnault's laboratory. During this time
he was successful in solving some very important and
fundamental problems in electricity.

As far back as 1834, W. Snow Harris had pubhshed
a paper in the Philosophical Transactions^ in which he
made a careful and thorough study of the elementary
laws of electricity. The results he obtained led him to
cast doubts on the laws which Coulomb had deduced
from his experiments, notwithstanding the strong
mathematical evidence which Poisson had given in
their favour. Snow Harris found, for instance, that in
several cases the laws of attraction between electrified
bodies did not follow the law of inverse squares —
that is, that the magnitude of the attraction was not
diminished to a quarter the value when the distance
between the centres was doubled. In some cases he
even found that the attraction between the electrified
bodies changed to repulsion at a certain distance. At
a particular distance he found that there was neither
attraction nor repulsion between them, although both
were electrified. As an experimentahst. Snow Harris's
reputation was of the highest, and the experiments
were all made with the minutest care. It required.

EARLY ELECTRICAL RESEARCHES 33

therefore, no little courage for William Thomson to
deny the truth of his conclusions, and to suggest that
he had omitted to take certain necessary precautions.

Snow Harris measured the electrical attraction be-
tween spheres by weighing them, and deduced an
empirical law for this attraction. Thomson suggests
that there must have been conducting bodies in the
neighbourhood of the bodies the attraction between
which was being weighed. In experiments of this
nature many precautions are necessary. " None of these
precautions, however, have been taken in the experi-
ments described in Mr. Harris's memoir, and the results
are accordingly unavailable for the accurate quanti-
tative verification of any law, on account of the numer-
ous unknown disturbing circumstances by which they
are affected." This plain speaking shows how convinced
Thomson was of the truth of the fundamental laws.

He gives in this paper, without proof, the theorem
of the attraction between two equal electrified spheres
when one of them is connected with the earth. Un-
deterred by the numerical labour involved, he computes
the forces that Snow Harris ought to have observed.
Instead of the attractions being 8*25, 4*6, and 35 grains
weight respectively, he calculates that they should
have been 7*94, 4*18, and 3'00 respectively. If Thom-
son's results are correct, therefore, the experiments
must have been done in a very careless manner.

Sir W. Snow Harris, however, did not admit the
accuracy of Thomson's criticisms, although his ana-
lytical skill filled him with admiration. He could not
point out what was wrong, but he knew that his experi-
ments had been made with the greatest care, and that
he had tried the effect on the weight required to balance
the attraction of bringing conductors in the neighbour-
hood of the electrified bodies. His opinions, therefore,

o

34 LORD KELVIN

were unchanged. In his Rudiments of Electricity, pub-
lished in 1848, he says, " The advance of modem re-
searches certainly renders the views of electricity
entertained by the French mathematicians somewhat
questionable. It is not that they cast the least doubt
on the intellectual ingenuity and profound thought of
the great experimentalist upon which their particular
theory is built, but only on the hjrpothetical evidence
upon which some of the experiments are based."

In the author's opinion, Thomson was not justified in
assuming that one of the spheres in Snow Harris's
experiment was at the same electrical pressure as the
earth. Making the much more probable assumption
that the electric charges on the spheres were equal and
opposite, and computing the attractions in Thomson's
way, he finds that the calculated values agree within
the Mmits of experimental error with the values observed
by Snow Harris. It is curious that no one seems to
have pointed this out before.

In 1849 Thomson sent a complete solution of the
problem of the mutual attraction or repulsion between
any two electrified spherical conductors to M. Liouville,
and in 1853 the solution was published in the Philoso-
phical Magazine. He employs an exceedingly ingenious
method, which he called the method of electrical images.
He says that it was suggested by Murphy's " principle
of successive influences." It is analogous to the optical
problem of calculating the illumination produced by a
candle placed between two spherical mirrors. The illumi-
nation is not only due to the direct rays from the candle
itself, but also to the rays proceeding apparently from
the infinite number of the images of the candle in the
two spheres. In an appendix to this paper he publishes
tables, which facihtate the utihsation of his results in
electrometers — that is in instruments for measuring

EARLY ELECTRICAL RESEARCHES 35

electrical pressures. The results obtained in this paper
give a perfect vindication of Coulomb's theory, and are
a marvellous illustration of Thomson's skill in bring-
ing the most difficult physical problems within the
domain of mathematical analysis.

In after years, Thomson made several successful and
some unsuccessful attempts to utilise his formulae for
the attractions between electrified conductors. At the
Crystal Palace Electrical Exhibition in 1890 he was
busy perfecting an instrument of this type for measur-
ing very high voltages. Unfortunately, at that period
there was practically no demand for an instrument of
this nature, and so he did not continue the experiments.
Professor W. Buchanan, his assistant at that time,
relates how Sir William Thomson frequently called to
find out the progress that was being made, and invari-
ably tested the experimental results obtained by the
formulae in his green-backed note-book.

Thomson's results give an absolute method of measur-
ing electrical pressure in volts. We have simply to
weigh the attraction between the conductors, measure
their dimensions and their distance apart, and then
Thomson's formulae give us the voltage. It will be
seen, therefore, that the volt is independent of all the
other electrical units. Similarly, he showed that the
ampere (the unit of current) could be found by weigh-
ing the attraction between two coils of wire in which
the same current was flowing. If we now adjust a
coil of wire so that when the current flowing through it
is one ampere (the difference of pressure between its
ends is one volt), we get a coil the resistance to the
flow of current through which is the unit of resistance —
that is, the ohm. In determining the ohm in this way,
any error due to a faulty knowledge of the value of
gravity at the place of observation cancels out. It wiU

36 LORD KELVIN

be seen that if we alter either our unit of length (the
centimetre) or our unit of time (the second), we must
also alter the three electrical units.

In 1853 Thomson read a remarkable paper to the
Glasgow Philosophical Society, on the " Oscillatory-
Discharge of a Leyden Jar," Six years previously,
Helmholtz had discussed a puzzling phenomenon he
had noticed when a knitting-needle was magnetised
by the discharge current from a Leyden jar passing
through a wire twisted round it. In some cases the
needle was left magnetised with the north pole at one
end, and sometimes with the north pole at the other.
A possible explanation of these results was that the
discharge was oscillatory. Thomson proved mathe-
matically that this was the case, and obtained a formula
by means of which the rapidity of the oscillations can
be computed.

A Leyden jar consists of a glass bottle coated inside
and outside with layers of tinfoil. When the inner and
outer layers are each connected with a terminal of a
frictional machine, charges of electricity are induced in
the two coatings. These charges are equal in magni-
tude but have opposite signs. If the extremity of a wire
connected with the outer coating be brought near a wire
connected with the inner coating, when they are suffi-
ciently close together a spark which makes a loud,
snapping noise ensues, and the quantities of electricity
in the two coatings are neutrahsed, a rush of electric
current taking place in the wires.

Helmholtz showed that an electric current cannot
rise instantaneously to a finite value. It requires time.
When an electric current flows, there is energy stored
up all round it. The energy due to the currents in the
discharge wires of a Leyden jar has been obtained from
the energy originally stored up by the charged coatings.

EARLY ELECTRICAL RESEARCHES 37

This transference of energy cannot be done instan-
taneously. When the coatings have lost all their electric
energy, then, if the mres had no resistance and no energy
was dissipated at the spark, the current in them would
be a maximum, and the energy of this current would be
exactly equal to the energy originally stored in the
coatings. As the current diminishes, this energy is
restored to the coatings, which are now charged in the
reverse direction, and, when the current stops, the whole
energy will have been stored up again in the jar. It
will now discharge in the reverse direction, the cycle
of operations being performed in the same order. In
practice, however, energy is dissipated at the spark
and in heating the wires, and so the oscillations only
ensue in certain cases, and get feebler and feebler until
there is not enough energy to start the current flowing
across the gap.

The phenomenon is analogous to the motion of a
pendulum swinging freely. If it be swinging in air,
the oscillations will gradually get smaller and smaller
until it stops. In this case the damping is said to be
small. If it were swinging in water, the damping would
be much larger, and if it were swinging in a heavy,
viscous Hquid Hke treacle, it would not oscillate at aU,
but, when displaced, would gradually move back to its
middle position without passing it. The resistance of
the electric circuit is analogous to the viscosity of the
liquid. When the resistance is very small the damping
of the oscillations is small, and when the resistance
exceeds a certain value we do not get an oscillatory
discharge at all.

Thomson suggested that an experimental verification
might be obtained by means of Wheatst one's revolving
mirror. Feddersen successfully did this in 1859. Re-
cently the invention of the oscillograph has enabled the

38 LORD KELVIN

discharge currents to be studied in detail, and Thomson's
mathematical formulae have been shown to be very ac-
curately true.

Thomson also suggested that as a Hghtning-flash was
the same as a Leyden jar discharge, but only on an
enormously greater scale, it was highly probable that
a hghtning-flash is an oscillatory phenomenon. This
would help to explain why hghtning-flashes which ap-
parently last for an appreciable time are sometimes
seen.

The main practical importance of Thomson's paper,
however, Ues in an apphcation which at that time was
undreamt of— namely to radio-telegraphy. When the
oscillations are very rapid, a large amount of the energy
stored in the jar can be radiated into space. Hertz
showed that these radiations can be detected by means
of a device called a detector. When the rays fall on
the detector, sparks ensue between two points of it.
This detector can only be used for short distances.
The discovery by Branly, in 1890, of another device
called a coherer enabled the radiated waves to be de-
tected to a much greater distance. The further dis-
coveries by Lodge, Marconi, and others have made
possible the everyday use of this system of signalling,
which is now a serious rival to telegraphy, and may
possibly even rival telephony in popularity. Thom-
son's beautiful theory which predicted the oscillatory
discharge of a Leyden jar induced many physicists
to study this phenomenon most carefully, and radio-
telegraphy is an immediate outcome of their labours.

HEAT AND WORK 39

CHAPTER V

INVESTIGATIONS INTO THE RELATIONS BETWEEN
HEAT AND WORK

At one of the meetings of the British Association in
1847 Thomson heard Joule read a short abstract of a
paper on the Mechanical Value of Heat. He was so
impressed by this paper that, v/ithout waiting for an
invitation, he rose and pointed out to the meeting the
great interest of the new theory and its practical im-
portance. This was the beginning of a lifelong friend-
ship between the two great physicists, and for many
years they jointly carried out experiments on the heat
effects of fluid motion.

Thomson worked assiduously for many years to perfect
the theory of heat engines. He perfected the theory
of the ideal heat engine first enunciated by the great
French engineer Carnot. This engine he looked on as
a device which takes a quantity of heat from a source
maintained ali a constant high temperature, converts
part of this heat into work, and then ejects the remainder
of the heat into a condenser kept at a constant low
temperature. In order that this engine be ideally
perfect, Thomson saw that it must be reversible. That
is, it must be able theoretically to take a quantity of
heat from the condenser, and after the expenditure of
a definite amount of work on the engine it must be able
to eject the original heat, together with the heat repre-
senting the mechanical equivalent of the work expended
into the source. He recognised that the amount of
work that- has to be done depends not only on the dif-
ference of temperature between the source and the

40 LORD KELVIN

condenser, but also on the absolute values of these tem-
peratures. For example, the efficiency of a perfect heat
engine working between the temperatures of 200° C. and
100^ 0. is not the same as that of a perfect heat engine
working between 100° C. and 0° C, but is decidedly less.;

He was thus led to invent his absolute scale of ther-
mometry (measurement of temperature). The abso-
lute temperature of the source is proportional to the
quantity of heat taken from it, and the absolute tempera-
ture of the condenser is proportional to the quantity of
heat ejected into it during a cycle. If these quantities
are measured, the relative magnitudes of the absolute
temperatures can be found, and hence also, by measur-
ing the difference of temperature between the source
and condenser, the zero from which they are reckoned.
This scale of thermometry is quite independent of the
physical properties of any physical substance, as, for
instance, the way in which mercury expands when
heated or the way in which the electric resistance of
pure platinum varies with the temperature. The scale
is defined in terms of the ideally perfect heat engine
alone. It is known as Thomson's absolute thermo-
dynamic scale.

Having found a true absolute scale to measure tem-
perature, the next thing to be done was to find the
relation between this theoretical scale and some easily
constructed practical scale. A gas thermometer would
be a suitable standard, provided that a gas which ex-
actly obeys Boyle's^ and Charles's^ law can be found.
Thomson and Joule, therefore, carried out many tests
to find how far any given gas obeys the ideal conditions.

^ When the volume of a given quantity of gas is doubled, its
temperature remaining the same, the pressure is halved.

2 The volume of a given quantity of gas increases by a definite
fraction of its volume for each degree of rise in temperature.

HEAT AND WORK 41

The method of experimenting devised by Thomson
was to force the gas in a steady current through a porous
plug and observe very accurately the temperature of
the gas on the two sides of the plug. In the case of
most of the gases that he and Joule examined, a slight
cooling effect of the gas was produced by forcing it
through the plug. It follows theoretically that the
absolute zero of temperature on Thomson's scale is
slightly higher than would be found by thermometers
formed by utilising the expansions of these gases to
construct a scale. With carbonic acid gas the cooling
effect was much greater than with air, nitrogen, or oxygen.
This might have been anticipated, as Regnault had
previously found that the ratio of increase in volume
-for a given rise in temperature is greater for carbonic
acid gas than for the constituents of air. They also
found that the higher the temperature of the gases
on which they experimented the smaller was the cool-
ing effect. Hence at high temperatures the dilatation
of the gas was more accurately proportional to the
temperature on Thomson's scale than at low tem-
peratures.

With hydrogen, however, they found that a contrary
effect was produced. When this gas was used, a sHght
heating effect was produced by forcing it through the
plug. The experimental investigation of the reasons
for these small differences of temperature proved to
be very difficult and laborious. The experiments were
carried out in Manchester. They were cut short by
the action of the owners of adjacent property, who
threatened Joule with legal proceedings, owing to the
vibration and noise caused by the experiments.

The results of these experiments were communicated
in a series of papers to the Royal Society. They proved
that the temperature of melting ice was 273*7° on Thorn-

42 LORD KELVIN

son's scale, and the temperature of boiling water was
373-7°. The experiments show that when a gas expands
at constant temperature it absorbs an amount of heat,
the mechanical equivalent of which is very nearly the
same as the work done during the expansion. In 1842
Mayer of Heilbronn assumed as a self-evident proposi-
tion that the work done was the exact mechanical
equivalent of the heat absorbed, and hence calculated
the mechanical equivalent of heat. If his data had been
accurate, this would have given a good approximation to
the true value, but the assumption he made could only
be justified by experiment. Joule and Thomson's ex-
periments prove that, to a first rough approximation, the
assumption is justified. They also determine approxi-
mately its Hmitations.

Many interesting incidental phenomena are discussed
in these papers, as, for example, the effect of fluid fric-
tion in drying steam issuing from a high-pressure boiler.
Clausius and Rankine (Thomson's colleague at Glasgow)
had independently made the discovery that when steam
is allowed to expand heat must be added to it if it is to
remain dry steam. It is difficult to reconcile this with
the fact that when steam escapes from a high-pressure
boiler into the open air through a small aperture it
remains dry. Thomson explains this by taking into
account the heat developed by the fluid friction of
the steam rushing through the aperture. The heat
communicated to the escaping steam thus keeps it
dry. Hence high-pressure steam sometimes produces
a much smaller scalding effect than low-pressure steam.

Another question discussed was : Does a mercury ther-
mometer placed in a strong draught of air read the
true temperature of the air ? The authors found that it
mil read a Httle too high. The explanation is that the
retardation of the air flowing past the bulb makes it

HEAT AND WORK 43

lose part of the energy due to its motion. This lost
energy is converted into heat, and some of it goes to
raise the thermometer reading. If the thermometer be
sheltered from a gale by being placed near the top of a
wall which is at right angles to the direction of the wind,
and if the air round it is at rest, then the thermometer
will indicate a higher temperature than when placed in
the blast. The explanation is that the heating of the
air by friction near the top of the wall is on a large scale
and affects the thermometer appreciably.

Thomson accepted the theory of the molecular struc-
ture of bodies. However homogeneous a substance ap-
pears to be, if a portion of it were magnified sufficiently,
it would be seen to consist of molecules, and thus it
cannot be really homogeneous. At ordinary tempera-
tures, also, it would be seen that the molecules are in
motion. The heat in the body is the energy of the motion
of its molecules. At the absolute zero of temperature
these molecules would be at rest, and the heat contained
in the body would be zero. Looked at from this point
of view, we see at once why there must be an absolute
zero of temperature, and also why the properties of
bodies change as we cool them down. For instance, we
have now very strong experimental evidence for saying
that at the zero of temperature the electrical resistance
of a wire would be absolutely zero. Hence miUions
of horse-power could be transmitted from any part of
the world to any other, or even from one planet to
another, by an infinitely, thin wire, provided its tem-
perature could be maintained absolutely zero.

To enable his students to picture the molecular con-
stitution of sohd, hquid, and gaseous bodies respectively,
Thomson used to give the following illustration. Imagine
a harbour full of small boats, so tightly wedged together
that they all kept the same relative places. The waves

44 LORD KELVIN

would cause the small boats to rub together, and the
bigger the waves the more violent this action. In this
case the boats would represent the molecules of a sohd.
At the zero of temperature they would be at rest. At
ordinary temperatures every molecule would be vibrat-
ing. If the boats were loosely packed together, so that
they could drift relatively to one another, but yet always
be in contact with many of their neighbours, this would
represent the molecules in a hquid. Any given boat
might drift from one part of the harbour to another,
but it would always be in contact with other boats.
Finally, if the number of boats was so few that they
drifted about by themselves over considerable distances
before they came into collision and bounded off from
another boat, they would represent the molecules of a gas.

In a gas, therefore, the path of a molecule would con-
sist of broken straight lines ; in a Hquid it would be
a curve, and in a solid it would merely be a vibration
to and fro about a fixed point.

In 1852 Thomson read a paper to the Koyal Society
of Edinburgh " On a Universal Tendency of Nature to
Dissipation of Energy." In this paper he enunciates
a very general scientific theorem. It will be easily
understood by considering a special case. Let us con-
sider the heat energy of an isolated system. The Con-
servation of Energy tells us that the total energy must
remain constant. The availabiHty of this energy to
the inhabitants, however, depends on the heat engines
they use. All these engines work by taking in heat at
a high temperature and rejecting it at a lower tempera-
ture. This rejected heat is of no value to the inhabit-
ants. If, initially, parts of the system are at a high
temperature and other parts are at a low temperature,
the temperature of the whole is continually being
equahsed by the conductive flow of heat taking place

HEAT AND WORK 45

in unequally heated solid bodies. In addition, radia-
tion and convective currents of heat in gases help to
make the temperature uniform. Hence, when these
processes which we see taking place around us — both
cooHng hot bodies and heating cold bodies — cease, the
heat energy will be unavailable to the inhabitants. In
the solar system we see this great law of the dissipation
of energy always at work, and hence that portion of
the energy of Nature which man can utilise is continu-
ally getting less and less.

He was careful not to apply his physical generalisa-
tions to biology. In his opinion, the real phenomena
of life infinitely transcend human science. He gave in
1875 the following illustration of the absurdities to which
we would be led if we bHndly apply physical laws with-
out considering their Hmitations. It is a well-known
law in dynamics that if at any instant the direction of
motion of every molecule of a body were reversed, but
the magnitude of the velocity kept exactly the same,
the body would move along the path it had come, and
at every point of its backward path its speed would be
exactly the same as when it passed through that point
in the forward direction. It is conceivable therefore,
on the materiahstic hjrpothesis, that if at any instant
the motion of every particle of matter in the universe
were reversed, the course of Nature from that instant
would be reversed for ever after. *' The bursting
bubble of foam at the foot of a waterfall would reunite
and descend into the water ; the thermal motions would
reconcentrate their energy, and throw the mass up the
fall in drops, reforming into a close column of ascending
water. Heat which had been generated by the friction
of solids, and dissipated by conduction and radiation
with absorption, would come again to the place of con-
tact, and throw the moving body back against the force

46 LORD KELVIN

to which it had previously yielded. Boulders would
recover from the mud the materials required to rebuild
them into their previous jagged forms, and would be-
come reunited to the mountain peak from which they
had formerly broken away."

If this materiahstic doctrine could be apphed to life,
Hving creatures would grow backwards with conscious
knowledge of the future, but no knowledge of the past.
But this is clearly incredible, and physical speculations
of this nature are utterly unprofitable. But it is far
otherwise with regard to speculations as to what would
happen when the velocity of every molecule of a material
system is reversed. In this case we get the full explana-
tion of the theory of the dissipation of energy.

In 1884 Thomson read an interesting paper " On the
Efficiency of Clothing for Maintaining Temperature."
He showed experiments which prove conclusively that,
if bodies are below a certain size, the effect of putting
a covering round them is sometimes to cool them. For
instance, if we have a bare wire, parts of which are sur-
rounded by transparent substances hke glass and mica,
and send an electric current through it, if the current
be great enough the bare parts of the wire become in-
candescent, but the parts covered by the transparent
substances are quite dark. This proves that the covered
portions are the cooler. The reason of this is that the
convection currents of air streaming round the con-
ductor carry away more heat from the covered than
from the uncovered portions of the wire, owing to their
greater diameter. Hence the heat generated in the
covered portion of the wire is carried away more quickly,
and its temperature is therefore lower. This theorem
has important practical appHcations in connection with
the lagging of steam pipes and with electric power
transmission along covered wires.

HEAT AND WORK 47

In 1902 Kelvin considered tlie problem of what the
nature of the mechanism is that maintains the human
body at about 98*4° F. A thermostat is a device which
automatically maintains a space at a uniform tempera-
ture. The probabihty is that the mechanism of the
human thermostat hes in the small blood-vessels in
which the combination of oxygen with the body tissues
takes place. It is not easy to see how the instrument
acts when the surrounding temperature is above 98*4,
and the air is saturated with moisture so that the per-
spiration cannot evaporate. It seems as if the surplus
heat must be carried away by the breath.

Kelvin subsequently came across a paper by Dr.
Crawford, published in the Philosophical Transactions
for 1781, and entitled " Experiments on the Power that
Animals, when placed in Certain Circumstances, possess
of Producing Cold." By experiments on a living and
dead frog, both of which were placed in hot flannel at
106° F., he showed that after five minutes the tempera-
ture of the Hving frog was only 78, whilst that of the
dead one was 81. The action of the vital power of the
hving frog was to generate cold. Kelvin suggests that
possibly in these circumstances there may be a surplus
of oxygen in the breath. More oxygen may be breathed
out than taken in. If this be found to be the case,
animal cold would be explained by the deoxidation
(unburning) of matter within the body. These experi-
ments are very difficult to carry out, but there can be
no doubt that, if successful, the results obtained would
be of great importance.

48 LORD KELVIN

CHAPTER VI

SUBMARINE TELEGRAPHY AND NAVIGATION

In the ten years between 1840 and 1850 great im-
provements were made in systems of land telegraphy.
During this period the mystery of the electric method
of signalling greatly stirred the popular imagination.
Every leading newspaper had a column headed " By
Electric Telegraph." People were beginning to reahse
that the close connection between science and engineer-
ing might lead at any moment to still greater marvels. In
particular, the possibihty of connecting the New World
with the Old by means of an electric cable was warmly
discussed, but its feasibihty as a commercial venture
was denied by many capable engineers.

The first submarine telegraph was laid between Dover
and Calais by a steam tug in August 1850. It consisted
merely of a copper wire insulated by gutta percha. No
protective sheathing or armouring of any kind was
used. It was not surprising, therefore, that the anchor
of a fishing smack cut it in two a few hours after it was
laid. During these few hours electricians had been
busy signalling through it. They had noticed that
the signals received were extraordinarily sluggish in
their action. They were quite different from the clear
and sharp signals received on land fines. This was ex-
plained by noticing that the fine must act fike the inner
coating of a Leyden jar and store electricity along its
length. In 1851 a cable was laid between Dover and
Calais, and in 1853 the British and Irish Magnetic Tele-
graph Company laid a cable between Port Patrick and
Donaghadee. These cables were practically success-

TELEGRAPHY AND NAVIGATION 49

ful, and were the forerunners of the ambitious schemes
for laying a cable across the Atlantic, in which Professor
WilHam Thomson played such a notable part.

In May 1855, when still a young man of thirty, he
published the solution of the problem of the transmission
of telegraph signals along a cable, and established what
is known as the inverse square law. For slow-speed
signalling his solutions still apply, but for rapid signal-
ling his solution has to be modified, so as to take into
account the electric inertia of the current.

Thomson's conclusions were questioned by Mr.
Whitehouse, who was interested in a project for an
Atlantic cable. The controversy with him probably
led Thomson to take a keener interest in submarine
telegraphy than he would otherwise have done. In
1856 the Atlantic Telegraph Company was formed, and
Thomson was appointed a director. In a letter to
Helmholtz in December 1856, he says that he is san-
guine about the success of the project. He points out
that, nearly all the way across, the bed of the Atlantic
consists of fine sand and microscopic shells. Its depth
nowhere exceeds three and a half miles. UnHke the
Mediterranean, there are no precipitous mountains or
deep ravines along the sea bottom. He also says that
" The practical men engaged have all the experience of
previous failures." Unfortunately, they had to experi-
ence several more failures before success crowned their
efforts in 1866.

In 1857 the British battleship Agamemnon and the
United States frigate Niagara started to lay the cable.
After 380 miles of the cable had been laid by the Nia-
gara, the cable snapped, owing to the inexperience of
the man in charge of the brakes. Thomson, who was
on board the Agamemnon, came back more enthusiastic

D

50 LORD KELVIN

than ever and full of ideas for improving" the engineer-
ing methods for laying cables. In the spring of 1858
he perfected a very sensitive instrument for detecting
currents. The instrument is known as the mirror gal-
vanometer. A minute mirror, Uttle bigger than a six-
pence, is suspended by a silk fibre, so that it hangs with
its plane vertical. Two or three pieces of magnetised
watch-spring cemented to its back make its plane point
to the Magnetic North and South, and at the same time
cause the plane to deflect when a current flows in a
coil of wire surrounding the mirror. The deflection
is observed by means of a ray of Hght which, after re-
flection from the mirror, falls on a graduated scale. If
this scale be some distance away from the mirror, it is
easily seen that a very minute deflection of the mirror
produces quite a large deflection of the spot illuminated
by the beam of Hght falling on the scale.

The same two ships started on another cable-laying
expedition in 1858. After experiencing very severe
storms and overcoming many practical difficulties, the
first Atlantic cable was laid. It connected Ireland with
Newfoundland. Mr. Whitehouse, who was in charge of
the Irish end of the cable, attempted for some days to
use his own signalHng apparatus, but with no success.
It is highly probable that the high electric pressures
which he had to employ with his method of signal-
ling weakened the insulation of the cable. He had
finally to fall back on Thomson's mirror galvanometer.
It was this instrument that prevented the cable from
being an absolute failure. The directors were dissatis-
fied with Whitehouse's management, and directed Thom-
son to take fuU control. Thomson's tests proved that
the cable was in a very precarious state, and after a
few weeks' troublous existence it broke down completely,
and became utterly useless.

TELEGRAPHY AND NAVIGATION 51

During its short life 732 messages had been sent, some
of which were of great importance. For instance, by its
means the orders for two regiments of Enghsh soldiers
to leave Canada in order to help to quell the Indian
Mutiny were countermanded. This is estimated to have
saved the country at least £50,000. It will be seen, there-
fore, that the results attained by this cable were not
merely of theoretical importance.

The experience gained was of the greatest value. No
further attempt was made until 1865, when the Great
Eastern was chartered to lay the cable. In the inter-
vening years Thomson was indefatigable, both in im-
proving theory and methods and in encouraging the
shareholders to make a fresh attempt. " What has
been done will be done again. The loss of a position
gained is an event unknown in the history of man's
struggle with inanimate Nature."

The 1865 attempt was a failure. After laying 1200
miles, the cable snapped. Its great weight baffled all the
attempts made to grapple it, and so the expedition was
unsuccessful. The engineers returned, however, full of
hope for the future. In the summer of 1866 not only
was a new cable laid, but the old one was recovered and
completed.

To Thomson belongs the credit of having done the
most to perfect the electrical part of the enterprise.
Along with Mr. Canning, the engineer of the company,
and Captain Anderson, of the Or eat Eastern, he received
the honour of knighthood. Four years later the mirror
galvanometer was replaced by the syphon recorder, an
instrument which draws a curve on a strip of moving
paper when messages are being sent. To this day the
recorder, with many improvements made by Thomson
himself, remains the standard instrument for submarine
telegraphic work.

52 LORD KELVIN

When the cables were first laid, the speed of working
was about eight words per minute. Subsequently the
speed was doubled by using condensers at each end of
the cable. At the start the tariff was £20 for twenty
words and £1 for each additional word. It is now only
a shilhng a word, and in the North Atlantic alone there
are sixteen cables. It was not until 1869 that Thomson
got any profits from the Atlantic Cable Company. The
first use he made of them was to found scholarships at
Glasgow University in experimental physics.

The experience gained when laying the Atlantic cable
and his association with engineers affected the tenor of
his Hfe. He entered into partnership with CromweU
Varley, a very able electrician, and Fleeming Jenkin,
the professor of engineering at Edinburgh University.
Varley perfected the method of using condensers at the
end of long cables, and Thomson and Jenkin perfected
the " curb " method of signalling. In this method
each signal current is followed up by a reversed current
of shorter duration. This both accelerates the rate at
which signals can be sent and makes them sharper.

Thomson made many important contributions to the
theory of navigation. The theory of compass devia-
tions was very thoroughly worked out by his friend,
Archibald Smith, and the results were incorporated in
the Admiralty Manual of Deviations of the Compass, A
study of Smith's work led up to the invention of an im-
proved compass. The standard ship's compass of 1873
had many defects. When the ship roUed, it was hable
to swing through a large angle. Thomson was the first
to see that, in order to neutralise the effects of the ship's
magnetism, the needle must be short. At the same time
the horizontal free swing must be very slow, otherwise
it will be unsteady. To prevent sticking also, the fric-
tion must be very small. To overcome these difficulties,

TELEGRAPHY AND NAVIGATION 53

he made the moving part of the compass of an aluminium
rim, having radial silk threads. Pieces of magnetised
knitting-needle were attached to the threads to act as
magnets. The whole moving part only weighed 180
grains, but its period of oscillation was longer, and the
friction error smaller, than that of the compass in use
at that period. The disturbing effect of the ship's
permanent magnets was overcome by using three sets
of correcting magnets. Two of these sets act horizon-
tally, and one vertically.

At the time of Lord Kelvin's death his compass was
practically universally used. In very large battleships,
however, owing to the large masses of magnetic material
in the immediate neighbourhood of the Kelvin compasses,
the difficulties of adjusting them are very considerable,
and their liability to get out of order is largely increased.
Recently attempts have been made to utihse the prin-
ciple of the gyroscope, which was first experimentally
verified by Foucault in 1852. He proved that a gyro-
scope which was free to move in two planes only will
tend to set itself with its axis parallel to the axis of the
earth. Its axis will therefore point to the true geo-
graphical north. The instrument, also, will be quite un-
affected by the magnetic masses of iron on board ship.
This is the principle of the Anschiitz gyro compass,
which is largely used in the German navy.

As far back as 1884 Thomson had attempted to reahse
in practice a gyro compass. Not only did he make a
gyrostatic model of a magnetic compass which pointed
to the geographical north pole, but he made also a
gyrostatic model of a dipping needle and a gyrostatic
balance for measuring the vertical component of the
earth's rotation. The models were not very satisfactory,
and so he devoted himseK to improving his magnetic
compass. In view of recent developments, it is inter-

54 LORD KELVIN

esting to recall how Thomson had partially explored
this field. In the Anschiitz compass the wheel makes
20,000 revolutions per minute, and its rotation is
maintained electrically.

Thomson's experience in cable-laying probably led
him to invent his navigational sounding-machine. The
method in use at that time was very laborious. A rope
an inch and a half in diameter, with a heavy sinker
attached, was employed. In deep water the ship had
to be stopped while the hne ran out, and while it was
being dragged in. Much time was lost, and a large
number of sailors had to be employed. Thomson saw
that most of the difficulties would be overcome by using
steel piano wire, which he knew to have very great ten-
sile strength. He demonstrated in the Bay of Biscay,
in 1872, that it was possible to take a sounding in 2700
fathoms with a 30-pound sinker attached to a steel
wire of No. 22 gauge.

When the ship is moving, the wire is no longer vertical,
and its length, therefore, is not a measure of the depth.
If the speed of the ship is known, it is easy to apply the
necessary correction. Thomson invented various kinds
of gauge, to enable accurate flying soundings to be taken
when the speed of the ship is not known. In one of
these the sinker contains a long, narrow glass tube, closed
at the top. The tube inside is coated with chromate of
silver. The deeper it sinks, the further the sea water
is forced into the tube. The distance it has been forced
up the tube can be seen by the discoloration of the coat-
ing, and the depth is read by placing the tube against
a suitably graduated scale. In the Kelvin sounding-
machine, now extensively used, the length of the cable,
which is made up of seven fine steel wires so as to secure
great flexibihty, is 300 fathoms. As the cable shps out,
a sailor presses a hght stick against it, and he feels at

TELEGRAPHY AND NAVIGATION 55

once the sudden change in the tension when the sinker
hits the bottom. The cable is then wound up by an
electric motor. It is customary to use two sounding-
machines, which are kept in constant operation near
the shore. They are also kept constantly going in
foggy weather when the depth is less than a hundred
fathoms. The use of these machines not only prevents
shipwrecks, but it also enables ships to sail at much
higher speeds in certain circumstances than would other-
wise be safe. They are therefore a great boon to navi-
gators.

Thomson considerably improved a method of deter-
mining the latitude and longitude of a ship at sea which
was devised by Captain Sumner, an American navi-
gator. If you measure the angular height above the
horizon at any instant of the Sun, the Moon, or a star,
then knowing Greenwich time by the chronometer,
you can find at what point on the earth's surface this
particular astronomical body was vertically overhead
at the instant under consideration. In this way it is
easy to determine a particular circle on the earth's
surface on the circumference of which the ship must he.
A second observation, taken later, determines another
circle on which the ship is now lying. These two circles
intersect in two points, one of which is near the true
position of the ship. In general, there is no doubt as
to which of the two points is the correct one, and hence,
by calculation, we can determine the true position of
the ship. In order to simplify the calculations, Thom-
son pubhshed Tables far Facilitating Sumner's Method at
Sea. The particular method Thomson advocated has
not come into general use, but it was a valuable contri-
bution to the theory of nautical astronomy.

When this method was first published. Sir George
Airy, who was then Astronomer Royal, wrote a letter

56 LORD KELVIN

to Nature criticising it. The letter was founded on a
misapprehension as to what the method really was.
J. A. Ewing (now Sir Alfred Ewing), who had helped to
calculate the tables, was indignant, as the criticism was
not vahd and would do harm. He therefore telegraphed
to Thomson asking his permission to answer it. Thomson
promptly telegraphed back, " Yes, by all means answer
in your own name, but don't hit too hard. Remember
he is four times as old as you."

Another invention of Thomson's which might be
mentioned in this connection is his tide-predicting
machine. By means of the data given by a self-record-
ing tide-gauge, the law governing the tides for a particu-
lar port is found out by mathematical analysis. The
machine can then be applied to predict all the future tides.
The machine is still in daily use at the National Physical
Laboratory for predicting tides at various ports.

CHAPTER VII

WAVES AJSTD VORTICES

Thomson made a hfelong study of the motion of fluids.
When taking a hohday on the Lalla Eookh, he was often
busy studying the motion of ripples and waves and
finding the laws which govern their motion. In a letter
written in 1871 to Froude (the great naval expert, who
was at that time studying the motion of ship models
in an experimental tank), he describes how he was led to
study the action of capillarity in modifying the motion
of waves. He relates how once on a calm day off Oban,
when the yacht was drifting at about half a mile an
hour, he studied the ripples formed by a fishing-liue,
with a lead sinker attached, hanging over the stern. The

WAVES AND VORTICES 57

line was preceded by a very fine and numerous set of
short waves. Streaming off at a definite angle on each
side were the well-known obhque waves, with the larger
waves following behind the Hne. The whole formed a
beautiful and symmetrical pattern, the key to which he
was fortunate enough to find.

He noticed that although the waves in front and in
the rear had different wave-lengths, yet they had the
same velocity. As the speed of the yacht slowed down,
the waves behind got shorter, and those in front got
longer. The speed diminishing still further, one set of
waves shorten, and the other lengthen, until they become
of the same length, and the angle between the obhque
lines of waves opens out until it becomes nearly two
right angles. At very slow speeds the pattern disappears
altogether. Thomson found that these results were in
exact agreement with, and could consequently have
been predicted from, his mathematical equations. He
calculated that the minimum velocity of the ripples
was 23 centimetres (9 inches) per second.

About three weeks later, when becalmed in the Sound
of Mull, he, together with his brother James and Helm-
holtz, actually measured this velocity, and so verified
his theory. Thomson suggested that disturbances the
wave-length of which was less than 1*7 centimetres (67-
hundredths of an inch) should be called ripples. The
name waves should be confined to disturbances having
wave-lengths greater than this. Adopting this sugges-
tion, we may say that ripples are undulations in which
the shorter the length from crest to crest the greater is
the velocity of propagation. For waves, on the other
hand, the greater this length the greater is the velocity
of propagation. The motive force for ripples is mainly
the capillary attraction (cohesion), but for waves the
motive force is their weight. Capillary attraction is

58 LORD KELVIN

the motive force which makes a dewdrop vibrate. The
effects of capillarity on the velocity of propagation of
waves can be neglected when the wave-length is greater
than two inches.

The introduction of cohesion into the theory of waves
enables us to explain the pattern of standing ripples seen
on the surface of water in a finger-glass, made to sound
by rubbing a moist finger on the Up. If gravity were
the only force, the wave-length for 256 vibrations per
second would be one-thousandth of an inch, which could
only be seen distinctly mth a microscope. Taking cohe-
sion into account, we find that for waves of the same
frequency the wave-length would be nearly eighty times
as great, which accords much better mth ordinary experi-
ence.

When the sea is perfectly calm, a shght motion of
the air — ^not exceeding half a mile an hour, or 8" 8 inches
per second — does not sensibly disturb the smoothness
of the reflecting surface. A gentle zephyr destroys
the perfection of the reflecting surface for a moment,
but when it departs the sea is left as pohshed as before.
When the motion of the air is about one mile per hour,
minute corrugations are formed on its surface, the effects
produced being like those produced by corrugated glass.
The fly-fisher well knows that they help to conceal him
from the trout. These ripples cannot propagate them-
selves, and parts of the surface sheltered from the wdnd
still remain smooth. When the wind attains a velocity
of two miles an hour, distinct small waves are formed.
A few ripples may, however, still be noticed sheltered
in the hollows between the waves. The vertical dis-
tance between the crest and hollow of these waves is
about an inch. If the wind increase, they become
cusped, and rapidly increase in size.

A peculiar phenomenon connected with canal navi-

WAVES AND VORTICES 59

gation furnished Thomson with a problem after his
own heart. In the days when there was a large pas-
senger traffic on the Glasgow and Ardrossan Canal
it was discovered that, above a certain critical speed,
the resistance the boat offered to motion through the
water greatly diminished. The discovery was made
accidentally. A spirited horse was once dragging a
boat containing one of the proprietors along the canal.
Taking fright, it suddenly started off at a gallop. The
proprietor noticed that at this speed the foaming stern
surge which did such damage to the banks of the canal
ceased. The vessel seemed to rest on the summit of
a progressive wave. The commercial value of this dis-
covery was apparent. Boats about 60 feet long and
6 feet wide were constructed of thin sheet iron. The
two horses which dragged the boat started slowly, and
then, at a given signal, they jerked it on to the top of
the wave, and set off at a rate of about ten miles an
hour. The method was also used on the Forth and
Clyde Canal, connecting Glasgow with Edinburgh. The
theory given by Thomson is complete and satisfactory.
At speeds greater than the critical speed no foaming
surge devastating the banks is formed, and therefore
the resistance to the motion is very much reduced.

The motion of vortices in hquids was a problem which
keenly interested Thomson. In Crelle^s Journal for 1858
appeared a classical memoir on the subject by Helmholtz,
He states mth admirable clearness the main laws which
govern their motion. Thomson took up the investiga-
tion where Helmholtz left it, and developed it much
further, wdth the object of making a complete mechani-
cal theory of the aether based on vortical atoms.

The motion of a whirlpool or a whirlwind is an example
of a simple vortical column with two endso A smoke
ring is an example of a circular vortex closed on itself.

60 LORD KELVIN

If we draw a semicircular plate rapidly through the water
for a short distance, we get a semicircular vortex w^th its
ends on the surface. Professor Tait of Edinburgh, who
collaborated with Thomson in writing the great treatise
to be described in the next chapter, invented a method
by means of which large smoke rings, containing a con-
siderable amount of energy, could be produced with ease
and certainty. Thomson used this method to illustrate
to his class the properties of vortex rings.

When two smoke rings hit one another, they rebound,
shaking violently from the effects of the shock, just as
if they were made of rubber. A very curious phenome-
non is observed when two coaxial vortex rings are moving
in the same direction. The leading vortex ring dilates
and moves more slowly, but the lagging vortex contracts
and moves more rapidly. The two rings apparently
attract one another. Hence the lagging ring overtakes,
and passes through, the first. The same actions take
place again, their roles being now reversed. These
actions can easily be observed with tobacco-smoke
rings or with the half-vortex rings made by dramng
a semicircular blade rapidly through the water.

When a vortex ring approaches a wall it expands.
At the same time its translational velocity slows do-^n,
but the rotational velocity of the molecules composing
it increases. Thomson explains this by his method of
images. We imagine the wall removed and an equal
vortex, the image of the first, to be approaching it.
The mutual action between them is repulsive; there-
fore their speed slows down, and it can be shown, from
dynamical principle, that they must expand.

If viscosity — that is, fluid friction — could be neglected,
a vortex, once started, would exist for ever. This at once
suggested to Thomson that the only true atoms of which
the universe is made are vortex rings. He considered

WAVES AND VORTICES 61

that the hard, impenetrable, spherical atom of Democritus
and Lucretius was a highly improbable assumption. In
years past it was, perhaps, a necessary assumption in
order to explain the unalterable distinguishing quahties
of different kinds of matter. Now that Helmholtz had
proved that the strength of a vortex filament moving
in a perfect fluid remains constant, the Lucretian hypo-
thesis can be abandoned. Vortex rings in a perfect
fluid would exist for ever. To generate them can only
be the action of a creative power.

The results obtained by spectrum analysis prove that
the ultimate constituents of simple bodies must be
capable of vibrating in one or more different ways.
In this respect they must be like a stringed instru-
ment having one or more strings, or a solid consisting of
one or more tuning-forks rigidly connected. Thomson
pointed out that, on the Lucretian hypothesis, we must
suppose that the molecule of sodium, for instance,
should consist of a group of atoms with void spaces
between them, as a single, infinitely hard, spherical atom
could not have one, and most certainly could not have
two free periods of vibration. It is difficult to con-
ceive, therefore, that a sodium molecule consisting of
several independent spheres could be stable and dur-
able. Hence it loses the one recommendation which
inclined philosophers to accept it provisionally.

Thomson proved that the vortex atom has perfectly
defuiite periods of vibration, which depend solely on the
motion which constitutes it. He thought it probable
that the atoms of substances did not consist merely of
simple vortex rings, but consisted of two or more vortex
rings linked together like the links of a chain. It is
easy to see that a vapour consisting of such atoms
would be probably capable of satisfying the very exact-
ing spectrum test.

62 LORD KELVIN

The theory is a great advance on Newton's corpus-
cular theory, as it is capable of explaining very abstruse
phenomena. Even during Newton's hfetime the many
arbitrary assumptions he had to make about his cor-
puscles in order to explain various phenomena seriously
discounted the value of his theory. Thomson at first
incHned to adopt the elastic sohd view of the sether,
but this he abandoned when he saw that the necessary
rigidity could be obtained more simply by imagining
an sether formed of vortex rings. Modern scientific
men are inchned to beheve that matter itself is but an
sethereal manifestation. Larmor, in the following pas-
sage, states this clearly, and points out some of the
difficulties in connection with the vortex atom theory.
" The fluid vortex atom faithfully represents in many
ways the permanence and mobihty of the sub-atoms of
matter ; but it entirely fails to include an electric
charge as part of their constitution. According to any
sether theory static electric attraction must be conveyed
by elastic action across the sether, and an electric field
must be a field of strain, which impHes elastic quality
in the sether instead of complete fluidity : the sub-
atom with its attendant electric charge must therefore
be, in whole or in part, a nucleus of intrinsic strain in
the sether, a place in which the continuity of the sether
has been broken and cemented together again (to use a
crude but eflective image) without accurately fitting
the parts, so that there is a residual strain all round the
place."

In later life, Kelvin made several interesting specula-
tions about electrons. He suggested, for instance, that
a positive electron is an atom which, by attraction,
condenses sether into the space occupied by its volume.
Similarly, a negative electron rarefies, by repulsion, the
sether remaining in the space occupied by its volume.

WAVES AND VORTICES 63

The stress produced in the aether outside two such
atoms by the attractions or repulsions which they exert
on the aether within them would cause apparent attrac-
tion between a positive and a negative electron and ap-
parent repulsion between two electrons, both positive
or both negative. It fails, however, to explain the New-
tonian law of the inverse square. No known or hitherto
imagined properties of elastic matter can explain this
by s cress of the aether. By making a certain assump-
tion as to the law according to which portions of the
aether act on one another, Kelvin showed that the phe-
nomena of electrical attraction and repulsion might be
explained. The great merit of this theory is that it does
not necessitate an aether transmitting both electric and
magnetic force. This assumption raises a difficulty in
the ordinary theory which Kelvin regarded as insuperable.

Making Kelvin's assumptions the main outstanding
difficulty is how the enormous attractive force between
magnetic poles can be transmitted by the aether. As-
suming that the density of aether is only the thousandth-
millionth part of the density of water and that the
velocity of light is 186,000 miles per second, Kelvin
calculated that the rigidity (being density multiplied
by the square of the velocity) of the aether was greater
than that of steel, and so it would be quite able to
transmit magnetic force.

Kelvin appreciated more fully than other men the
importance of discovering the mechanisms by means
of which electric and magnetic force are transmitted
through the aether. When the nature of these mechan-
isms are discovered there will probably be a gigantic
advance made in the practical applications of electricity.
The discovery of radio-activity in Kelvin's later years
opened up many new and unfamiliar aspects of the
problem, and made necessary many modifications of

64 LORD KELVIN

previous hjrpotheses. It soon became obvious that
extended experimental investigations were desirable
before any definite theory was formulated. Kelvin
contented himseK with pointing out the dangers of
deducing general laws from a few obscure phenomena
and showing how some of the older theories could be
modified to explain the new facts.

CHAPTER Vin

THOMSON AND TAIT'S "NATUBAL PHILOSOPHY"

P. G. Tait, of Edinburgh, was Senior Wrangler seven
years after Thomson took his degree. Like Thomson,
he had gone to St. Peter's College and coached with
Hopkins. In 1860, therefore, when he was elected to
the Chair of Natural Philosophy at Edinburgh University,
there were many points of similarity between his career
and Thomson's. Tait was the first to plan the great
literary undertaking of writing a complete treatise on
Natural Philosophy. He was surprised and dehghted
when Thomson suggested that they should write the
treatise jointly. They started with the intention of
discussing in succession the various branches of Natural
Philosophy, both experimentally and mathematically.

In 1867 the Clarendon Press pubhshed the first
volume of the series. It was mainly introductory, and
gave a very complete account of the Science of Force
(Dynamics) and its action in maintaining rest or pro-
ducing motion. The treatment of the subject is founded
on that given by Newton in his Principia, and the book
marks the beginning of a new epoch in dynamical
science. The high standard they set themselves made
it necessary to solve many difficult and abstruse

"NATURAL PHILOSOPHY" 65

problems. Owing to the large encroachments this
made on their time, they soon saw that it would be im-
possible for them to complete their great undertaking.

In 1872 Thomson pubhshed his Beprint of Papers on
Electricity and Magnetism. In 1879 the Cambridge
University Press published the first part of a new
edition of the first volume of their Natural Philosophy,
revised and greatly enlarged. In 1883 the second part
of this volume was published, under the editorship of
G. H. Darwin. In the preface the authors state that
they have definitely abandoned their intention of writ-
ing a complete treatise. They have, however, left in
the references to future volumes, as their method of
treatment can only be fully justified by taking into
account the original design of the work.

The first sentence of Fourier's Theory of Heat is
printed in the original French at the top of their preface.
" Primary causes are unknown to us ; but they are
subject to simple and constant laws, which may be
discovered by observation, and the study of which is
the object of natural philosophy." The first two para-
graphs of their preface explain very clearly the aim
they had in view,

" The term Natural Philosophy was used by Newton,
and is still used in British universities, to denote the
investigation of laws in the material world and the
deduction of results not directly observed. Observation,
classification, and description of phenomena necessarily
precede Natural Philosophy in every department of
natural science. The earlier stage is, in some branches,
commonly called Natural History ; and it might with
equal propriety be so called in all others,

" Our object is twofold : to give a tolerably complete
account of what is now known of Natural Philosophy,
in language adapted to the non-mathematical reader ;

E

66 LORD KELVIN

and to furnish to those who have the privilege which
high mathematical acquirements confer, a connected
outhne of the analytical processes by which the greater
part of that knowledge has been extended into regions
as yet unexplored by experiment."

Before the publication of this treatise many beheved
that the work done against friction was absolutely lost.
Newton beheved this. The authors, taking as a physical
axiom that " the Perpetual Motion is impossible," prove
the great principle of the conservation of energy.
Energy, hke matter, is indestructible. Thej'" point out
that every motion which takes place in Nature meets
one or other of the following forms of resistance —
sliding friction, viscosity or imperfect elasticity, re-
sistance due to induced electric currents, and resistance
due to varj^ng magnetisation. Our everyday experi-
ence proves that bodies falling freely in the air are
impeded by viscosity, and that friction greatly hampers
the action of all kinds of mechanisms.

The analogies of Nature lead us to beheve that every
star and every body of any kind has its relative motion
hindered by the medium in which it moves. A curious
result is that this frictional resistance tends to shorten
the year, for it makes the earth move closer to the sun,
and so the attraction between them is increased and
the year thus shortened. Astronomical data prove that
this shortening is appreciable, although very minute.
A fraction of the year, therefore, cannot be used as our
unit of time. Neither is the time of rotation of the
earth round its axis a constant. Newton explained
clearly the action of the sun and moon in producing
tides. Kant was the first to point out that the fric-
tional resistance to the motion of the tidal waters in
oceans, lakes, and rivers acts as a brake on the earth's
motion of rotation. It thus tends to equahse the lunar

"NATURAL PHILOSOPHY" 67

month — that is, the period of the moon's rotation round
the earth with the sidereal day — that is, the period of
the earth's rotation round its axis. The authors make
interesting speculations as to what will happen in the
future, taking into account also the effect of the solar
tides. They conclude that the moon is moving gradu-
ally further from the earth, and that the lunar month
is lengthening. After attaining a maximum distance
from the earth, it will then gradually return to the earth
in a spiral path, the month shortening, and it will finally/
fall on the earth. Sir G. H. Darwin has carried this inves-
tigation much further, making use of it even to calculate
the age of the earth. Starting with a planet in a partly
solid and partly fluid condition and rotating round its
axis in from two to four hours, he shows that the motion
is unstable. It is, therefore, higlily probable that it
spHt into two, the larger portion being the earth and the
smaller the moon. He then traces the relative motion of
the earth and moon up to the present day, and computes
that the minimum time required for the moon to
have attained its present distance is fifty-four million
years.

The data for making these calculations are somewhat
uncertain, but there can be no doubt as to the ultimate
result. All the bodies of the solar system must ulti-
mately fall together into one mass, which, although
rotating for a time, must finally come to rest relatively
to the surrounding medium.

Since neither the period of the earth's rotation round
the sun nor round its own axis can be considered constant,
the authors consider the question of the best standard
of accurate chronometry. Their first suggestion was
to make a metalhc spring and hermetically seal it in
an exhausted glass vessel. In their second edition they
mention Clerk Maxwell's suggestion that a period of

68 LORD KELVIN

vibration of an atom of hydrogen or sodium would be
an excellent natural standard. These atoms are all
ready made ; there is an infinite number of them aU
exactly alike in every physical property, and the time
of vibration of an atom as determined by spectrum
analysis is absolutely independent of its position in the
universe. Clerk Maxwell also suggested to the authors
that the time of revolution of an infinitesimal satellite
close to the surface of a globe of water could be ad-
vantageously taken as the unit of time, as it is quite
independent of the size of the globe.

The authors lay great stress on the importance of
experiments. They point out that, without experi-
menting, terrestrial magnetism would never have been
discovered. The same is true of the connection between
a lightning-flash and the phenomena exhibited by rubbed
amber.

They give rules for the conduct of experiments, and,
judging from their own very extensive experience, they
say that endless patience and perseverance in designing
and trjdng different methods for investigation are
necessary for the advancement of science. The ex-
perimenter who is Hkely to succeed is the one who does
not allow himself to be disheartened by the failure of
an experiment, but immediately sets about to vary his
method so as to interrogate Nature in every conceiv-
able way.

They follow Herschel in pointing out the importance
of residual phenomena. If, after making allowance for
aU known causes of error, there stiU remains an ap-
preciable discrepancy, it is of the greatest importance
to investigate the reason for this. Adams and Le
Verrier were led to discover a new planet by noticing
very shght anomalies in the motion of Uranus. Schon-
bein was led to discover ozone — a gas of great chemical

"NATURAL PHILOSOPHY" 69

activity — hy noticing that a frictional electrical macMne
produced a distinct smell when working.

On the other hand, when the agreement between our
results is closer than we have a right to expect, it is
probable that our apparatus is not trustworthy. For
example, a very good achromatic telescope makes every
star appear to have a sensible disc. But it would
be rash to draw any conclusion as to the size of the
star from this. Further investigation proves that it is
merely a phenomenon of the diffraction of light.

Until we know thoroughly the nature of matter and
the forces which produce its motion, it is impossible to
get rigorously exact solutions of physical problems. In
order to obtain solutions, we introduce limitations into
the problem. The authors, for example, take the case
of a crowbar used to move a heavy mass. We first of
all imagine that the bar is perfectly rigid, and obtain
an approximate solution. We next suppose that it
bends slightly, and so obtain a more accurate solution.
Next, supposing that the mass is perfectly homogeneous
— which, owing to its atomic constitution, it never can
be — and that the forces consequent on dilatation, com-
pression, and distortion are in exact proportion to these
deformations, we can get a still more accurate solution.
The complete discussion would involve the discussion
of the deformations which take place in every part of
the bar, fulcrum and mass, and we should also have
to take into account the heat generated and its con-
duction throughout the mass. Our ignorance of the
nature of matter maizes any such discussion impossible.
But in many cases solutions of great importance in
practical work can be obtained by limiting the gener-
ality of the problems in the ways shown by experiment
to be permissible.

It is interesting to notice that the proof the authors

70 LORD KELVIN

give that a sphere attracts an external particle as if
all its mass were collected at its centre is purely geo-
metrical, and is practically identical with that given by
Newton. Several terrestrial apphcations of Newton's
law of gravitation are given. The attraction of a hemi-
sphere on a particle at its edge is found. The result is
used to compute the deflection produced by a hemi-
spherical hill on a plumb-hne at its base. Similarly,
near the edge of a hemispherical cavity an opposite
effect would be produced on the plumb-Hne.

The more important theorems discovered by Thomson
in the theory of elastic solids are incorporated in the
second part of the treatise. Many of these problems
are of very great difliculty, and the results arrived at
by very powerful and neat analytical methods are of
great importance. It is an excellent introduction to
the advanced theory of the subject.

One of the problems solved is to find the deformation
of the solid earth, supposed to be a homogeneous sphere,
by the tides produced by the moon and sun. Thomson
was the first to point out that in any complete theory
of the tides this deformation has to be taken into ac-
count. All previous dynamical investigations of tidal
phenomena and of precession and of nutation proceeded
on the assumption that the outer surface of the soHd
earth is absolutely unyielding. In Thomson's opinion,
the mere fact of the existence of tides disproves the
hypothesis formerly commonly made that we live on a
mere thin shell of sohd substance enclosing a fluid mass
of melted rocks and metals.

If the earth were a thin shell covered mth a thin
layer of lighter liquid, the liquid would have practi-
cally the same depth all round. Under tidal influences,
it would simply rise and fall with the shell, and so the
tides would be infinitesimal, land and sea rising and

"NATURAL PHILOSOPHY" 71

falling together. He calculates that a solid steel sphere
of the size of the earth would yield one-third as much
as a perfectly fluid globe. This yielding would reduce
the height of the tides to two-thirds what it would be
if the rigidity were infinite. Sir George Darwin has
pursued this investigation further, and has obtained
interesting results.

The case when the liquid surrounding the globe has
a greater density than the globe itself is interesting, as
it leads to unexpected results. The discussion shows that
the equiUbrium in this case is unstable, but the complete
investigation still baffles the skill of mathematicians.

Thomson considered the augmentation of the tides
due to the mutual gravitation of the water on itself.
The results show that it is appreciable. Robison had
pointed out previously that the great tides in the Bay
of Fundy would produce a very sensible deflection of a
plumb-line in the neighbourhood. As this is due in-
directly to the attraction of the moon, it is not correct
to say that the attraction of the moon has no appreci-
able effect on the deflection of a plummet. Even ordi-
nary tides must produce at places near the sea an
effect on the plummet considerably transcending the
direct effect of the moon. The suggestion is made that
observation of this effect might be used to determine
the earth's mean density. In order to show Thomson's
keen insight into physical phenomena, his discovery of
a thermodynamic acceleration of the earth's rotation may
be mentioned. It is well known that the barometer in-
dicates variations of pressure during the day and night.
The semi-diurnal constituent has its maximum values
about 10 A.M. and 10 p.m. respectively. The crest of
the nearer tidal protuberance is thus directed to a point
of the heavens westward of the sun, and the solar at-
traction on these protuberances causes a couple about

72 LORD KELVIN

the earth's axis, which accelerates its rotation. As the
barometric oscillations are due to solar radiation, it
follows that the earth and the sun form a kind of heat
engine. Thomson calculates that the earth gains about
2*7 seconds per century on a perfect clock. On the one
hand we have this effect and the shrinkage of the earth
tending to make the earth rotate more quickly, and on
the other we have the tides and the fall of meteoric
dust tending to lengthen it.

Looking back on the work done by Thomson, there
can be httle doubt that, from the point of view of scientific
and engineering progress, the authors did well to abandon
the major portion of their undertaking. Much of the
work they originally planned has been excellently done
in special treatises. We need only mention Maxwell's
Electricity and Magnetism, Rayleigh's Sound, and Lamb's
Hydrodynamics. Had they proceeded with their under-
taking, there would have been considerable overlapping
with these works. The demands that would have been
made on Thomson's time would have seriously crippled
his work, and there is little of this that could be spared,
wdthout a loss which would probably outweigh the ad-
vantages that would accrue from having a complete
treatise.

CHAPTER IX

THE AGE OF THE EAUTH AND THE COOLING OF

THE SUN

In 1862 Thomson pubhshed two epoch-making papers.
The paper on the secular cooling of the earth was pub-
hshed in the Transactions of the Edinburgh Royal
Society, and the paper on the age of the sun's heat

THE AGE OF THE EARTH 73

was published in MacmillarCs Magazine. Both of these
papers were considered so important that they were
pubhshed as appendices to Thomson and Tait's Natural
Philosophy. They were read with dehght by physicists,
but geologists and biologists regarded them as uncon-
vincing. Huxley was the great advocate of the latter
class, and his attack elicited a brilhant and spirited
rejoinder from Thomson.

Hutton, Playfair, and Lyell taught what Thomson
called the doctrine of eternity and uniformity in geology
as opposed to the cataclysmal doctrine, which predicted
great disturbances and tremendous differences of climate
in past ages. Playf air, the brilliant advocate of Hutton's
theory, says that in the planetary motions we discover
no mark either of the commencement or the termina-
tion of the present order of things. Thomson totally
disagreed with this. He points out that Newton in
his Principia says that planets and comets keep their
motions a long time because the space in which they
move offers little resistance. The motion of comets
proves that it offers some resistance, and hence changes
are continually going on in the solar system. Laplace's
nebular hypothesis and other astronomical theories have
a cataclysmal basis. This is common knowledge. Pope,
for instance, says :

" Who sees with equal eyes as God of all,
A hero perish, or a sparrow fall,
Atoms or systems into ruin hurl'd,
And now a bubble burst and now a world."

Even the great Charles Darwin demands hundreds
of millions of years in his geological periods. It is of
great importance, therefore, to study Thomson's reason-
ing, and see how far he has been successful in putting
limitations to the periods of time demanded by geologists.

74 LORD KELVIN

It is universally admitted that at one period of time the
earth must have been a rotating, molten mass. If we
assume that this mass is practically homogeneous, it is
not difficult to calculate the shape that it would assume.
The shape would be approximately spherical, the poles
being flattened and the equator protuberant. Now,
when the earth solidified, it would probably retain the
same shape as it had when molten. But this shape
depends on the velocity of rotation, and hence geodesic
measurements enable us to compute this velocity. The
polar diameter is known to be 26*7 miles less than the
equatorial diameter. On the given assumptions it can
be shown that this is the shape that a hquid mass the
size of the earth would have if rotating at its present
rate. If the liquid mass were rotating at twice this
rate, it would be distorted from the shape of a sphere
four times as much. In addition, if it cooled when rotat-
ing at this rate, it is highly probable that all the conti-
nents would have formed a dry belt round the equator,
and that the poles would be the central points of the
polar oceans. The mere fact that we have no dry equa-
torial belt limits the velocity of rotation when the earth
was solidifying.

Kant was the first to show that the tides must act as
a brake on the earth's rotation. Adams and also Thom-
son and Tait calculate that the time of the earth's
rotation increases by twenty-two seconds every century.
Taking this figure, we see that 7200 milhon years ago
it would have been rotating twice as fast. Its shape
therefore proves that it could not have sohdified at this
period.

Taking into account all the uncertainties in the figures
and calculations, Thomson concludes that 5000 million
years ago the earth was certainly not solid, and that
it wa>s probably not solid even 1000 milhon years ago.

THE AGE OF THE EARTH 75

It will be seen that the reasoning is cogent, and so the
conclusions cannot be lightly disregarded.

Another method of determining the age of the earth
is by finding the rate at which it is cooling, and then by
Fourier's solutions calculate backwards to the time when
the earth was molten. Thomson was particularly at-
tracted by this method. From a survey of under-
ground temperatures in different parts of the world,
it is found that on the average the temperature of the
earth increases one degree Fahrenheit for every fifty
feet of descent. Heat, therefore, must be continually
flowing from the earth's interior to its surface, and,
since the earth's surface does not get hotter, there must
be a continual loss of heat from year to year from the
surface of the earth. The earth, therefore, must be
either getting cooler from age to age, or some temporary
dynamical action inside the earth must be keeping up
the heat. Thomson considered it proved that there
was less volcanic action in the earth now than there
was a thousand years ago — just as a battleship has less
ammunition on board after it has been discharging shot
and shell for several hours.

The chemical hypothesis to account for underground
heat would be probable if the rise of temperature as
we go downwards occurred only in isolated locahties.
The suggestion that there may be some slow uniform
combustion going on at a great depth under the sur-
face he thinks highly improbable. Poisson's hypothesis
that the present underground heat is due to a passage
at some former period of the solar system through
hotter stellar regions is only tenable if there was a well-
marked period of discontinuity in palaeontology. Thom-
son calcula^tes that if this passage took place between
1250 and 5000 years ago, then, in order to account for
the present underground temperature gradient, the

7Q LORD KELVIN

temperature of the supposed stellar region would have
to be from 25° to 50° F. hotter than the present mean
temperature. Hence there would have been plenty of
evidence available of such a phenomenon. The further
back we place this passage of the earth, the hotter the
stellar region would have to be. If the passage took
place more than 20,000 years ago, the excess of tempera-
ture would have been greater than 100° F., and so
animal Hfe would have been destroyed. As no evidence
has ever been deduced to support this, the hjrpothesis
is untenable.

Following Leibnitz, he assumes that the earth was
once an incandescent hquid sphere. Assuming that
the heat constants of this mass are the same as the
constants he and Forbes found by experiments on rocks
from a quarry near Edinburgh, and making allowances
for the uncertainty as to his data, he concludes that
the period of time since the earth soHdified lay between
20 and 200 million years.

After the beginning of the crusting over the terres-
trial heat would have httle direct influence on chmate.
After 40,000 years the rise of temperature as we bore
downwards would be about 1° per foot, after 160,000
years it would be half a degree per foot, and after 100
million years it would be the fiftieth part of a degree per
foot, which is the temperature gradient at the present day.
" Is not this, on the whole, in harmony with geological
evidence rightly interpreted ? Do not the vast masses of
basalt, the general appearances of mountain ranges, the
violent distortions and fractures of strata, the great pre-
valence of metamorphic action (which must have taken
place at depths of not many miles, if so much) all agree in
demonstrating that the rate of increase of temperature
downwards must have been much more rapid, and in
rendering it probable that volcanic energj^, earthquake

THE AGE OF THE EARTH 77

shocks, and every kind of so-called Plutonic action
have been, on the whole, more abundantly and violently
operative in geological antiquity than in the present
age?"

Thomson imagined that the interior of the earth was
like a honeycombed solid, the liquid always tending to
work its way up, owing to its lower specific gravity. The
actions that would take place in such a mass would
be sufficient to account for geological phenomena like
earthquakes, subsidences and upheavals and eruptions
of melted rock. The oceans on the surface of an earth
built up in this way would exhibit the phenomena of
tides «

In 1899 Kelvin, having the advantage of more accurate
data, stated that he agreed with Clarence King in think-
ing that the time since the earth was molten was about
twenty-four million years. This estimate, however, is
generally considered to be too small. Perry has pointed
out that if the conducting power of the material near
the centre was greater than that of the material near
the surface, Thomson's estimate would have to be raised
very considerably.

The discovery of radio-activity throws grave doubts
on the possibility of determining the age of the earth
from the known temperature gradient of its crust.
Curie has calculated that the heat emitted per hour
from one pound of radium would raise a pound of water
from the freezing to the boiling point. R. J. Strutt
has detected radium in many rocks of the earth's crust
in sufficient quantity to account for the temperature
gradient without the necessity of making any hjrpothesis
about heat being conducted from the interior. In fact,
if the crust were more than forty-five miles thick, the
outflow of heat would be greater than that actually
observed. We have even to suppose that inside the crust

78 LORD KELVIN

there is no radium. But, nevertheless, Thomson's de-
ductions mark an epoch in our knowledge of the world's
scientific history, and have stimulated and encouraged
many physicists to follow up his investigations.

Thomson's paper on the age of the sun's heat is divided
into three parts. In the first part he discusses the cool-
ing of the sun, in the second part, the present tempera-
ture of the sun, and in the third, the origin and total
amount of the sun's heat. He begins by pointing out
that we cannot be certain that the sun is losing heat at
all. It is quite conceivable that the heat generated by
the influx of meteoric matter may compensate for the
loss of heat by radiation. It is also conceivable that
it is an incandescent liquid mass, the heat of which is
due to the influx of meteors in bygone ages. The heat
generated by the influx of meteoric matter at the present
time may be neghgibly small compared with the heat
radiated. Spectrum analysis proves that the sun's
substance is very like the earth's. From Herschel's
and Pouillet's investigations, he concludes that the rate
at which heat is radiated from a square foot of the
sun's surface is 7000 horse-power. It would be in-
credible to suppose that the sun had existed for countless
ages radiating heat at this rate. He supposes that the
sun was formed by the falling together of a large number
of smaller bodies by mutual gravitation. The energy
of the motion lost by the coUision would all be converted
into heat.

Making certain assumptions about the specific heat
of the mass of the sun, he calculates that probably it
has not illuminated the earth for 100 million years,
and almost certainly that it has not illuminated it for
500 million. He concludes that the inhabitants of the
earth cannot continue to enjoy the fight and heat
essential to their fife for many milfion years longer.

ELECTRICAL ENGINEER 79

" unless sources now unknown to us are prepared in
the great storehouse of creation."

The discovery of radium makes it necessary to modify
this calculation also. It is true that an examination
of the sun's spectrum has not, so far, revealed any
radium lines, but it is well known that helium, a trans-
formation product of radium, is present. It is probable,
therefore, that there is radio-active matter in the sun.
It is possible that Thomson's estimate may be a hundred
times too small.

CHAPTER X

ELECTRICAL ENGINEER

The industry of electric lighting and power distribu-
tion is immensely indebted to Lord Kelvin. In the early
days he advocated enthusiastically the use of the electric
light, emphasising its many advantages. He also used
aU his influence to remove the legislative restrictions
which at that time seriously hampered the industry.
As far back as 1874, Sir Wilham Thomson was President
of the Society of Telegraph Engineers. When the title
of the Society was changed to that of the Institution
of Electrical Engineers, he was chosen as the first presi-
dent. He was president for the third time in 1907 —
the year of his death.

In 1877, when a juror at the exhibition in Philadelphia,
he wrote an appreciative report on the exhibit of Gramme
D3niamos. The method invented by Werner von
Siemens ten years previously of using electro-magnets,
which were excited automatically when the machines
were running, was employed. Thomson saw at once
that the abolition of permanent magnets was a great

80 LORD KELVIN

step in advance, and he started formulating the mathe-
matical theory of their working. This theory was
generalised later in the classical paper by J. and E.
Hopkinson, published in the Transactions of the Royal
Society in 1886.

In a discussion on a paper read to the Institution
of Civil Engineers in 1878, Thomson pointed out the
feasibihty of conveying electric energy to a distance of
several hundred miles. The " economical and engineer-
ing moral " of the theory was that the towns of the
future would be illuminated by electricity generated
at electric stations near the pit's mouth, where the coal
dross, most of which was at that time wasted, could
be used for working engines of the most economical
kind. Electrical engineers will recognise how closely
this prediction has been fulfilled. There are now many
power stations aU over the world, where electricity is
generated in " bulk " and transmitted considerable
distances for lighting purposes.

He did not fail to foresee that waterfalls would soon
be harnessed to provide power for industrial purposes.
Werner von Siemens had mentioned to him in conversa-
tion that the power of the Falls of Niagara might be
transmitted electrically to a distance. The idea might
well strike them as fantastical. Only a year before
the telephone and the phonograph would have been
classed as equally chimerical. There could be no ques-
tion about the " vast economy " effected by harnessing
Niagara.

In 1879, one year after the lighting of the London
embankment by Jablochkoff candles — the current for
which was furnished by Gramme dynamos — Thomson
gave evidence before a Parliamentary Select Committee,
which had been appointed to consider the question of
electric Hghting. The evidence he gave proves the

ELECTRICAL ENGINEER 81

thorough grasp he had of the whole subject, both from
the scientific and the commercial point of view. He
mentioned that the experiments made by Messrs.
Siemens and at Edinburgh University proved that
one horse-power would produce 1200 candles of visible
electric light. The electric light, therefore, would soon
be used even in the passages and staircases of private
dwellings. It was much more economical than gas.

Arc lamps might be put on iron poles 60 feet high,
or the old French plan of span wires might be used.
There was no need to employ globes of opal glass absorb-
ing half the light generated. From the hygienic point
of view, the electric light was much preferable to gas.
As a mathematician, he saw nothing impossible in sub-
dividing the electric light. As a motive power, he
could see no limit to the applications of electricity. It
could do all the work now done by steam engines, no
matter how powerful they were. The duty of legislators
was to encourage inventors to the utmost.

The abstract of this evidence, which appeared in
Nature for May 29, 1879, concludes with the sentence,
" This may be called the fanatical view of electric light."
At the present day it reads merely like a plain record
of the facts. As a matter of history, this evidence was
instrumental in turning the attention of certain finan-
ciers and young engineers to developing the practical
apphcations of electricity.

The invention by Faure, in 1881, of a battery (accumu-
lator) by means of which electricity could be economi-
cally stored, again roused Thomson by its many possi-
bihties of usefulness. In letters to the Times and to
Nature, he points out that this discovery is a great step
in advance. It will now be possible to use " Swan or
Edison " lamps both for mast-head lights and for the
red and green side-lamps. He also makes the important

82 LORD KELVIN

statement that accumulators could be used for traction
purposes. To drive a car by electric motors would be
more economical than to employ horses. During this
year at the British Association Meeting he explained
how accumulators would prove to be an invaluable
adjunct in country-house hghting. He also enunciated
his law for determining the size of the mains to be used
for electric Hghting, so that the distribution should be
made with the maximum economy.

At the same meeting he proved the law govern-
ing the efficiency of a dynamo, and gave la simple
formula by means of which the load at which the
efficiency is a maximum can be found. This law is
well known to dynamo designers. In conjunction also
with his nephew and colleague, J. T. Bottomley, he
gave the results of tests which they had made on the
illuminating power of glow-lamps. They measured
the rate at which electric energy was supplied to the
lamps and the illumination produced. They were thus
able to find the hght produced by a given amount of
energy, and hence compare the efficiencies of the lamps.
The principle of the method is the same as that now
employed in every lamp factory in the world.

In 1881 Thomson patented a special winding for an
alternating current djmamo. Ferranti independently
invented an improvement on this design. They there-
fore entered into a working agreement, and this associa-
tion was influential in turning Thomson's attention to
many of the important problems then occupying the
minds of electrical engineers.

In connection with the practical difficulties experi-
enced at the start of the London Electric Supply Cor-
poration, Ferranti often consulted him. This company
transmits power from Deptford to Trafalgar Square,
London, at a pressure of 10,000 volts, and the experience

ELECTRICAL ENGINEER 83

gained by the working of this pioneer company has been
of great value to the electrical industry. One of the
problems Thomson solved was the distribution of the
current over the cross section of a conductor carrying
a rapidly alternating current. His results show that
in some cases the current does not penetrate far into
the conductor. It is confined merely to a thin skin of
the conductor. So far as current-carrying is concerned,
the great bulk of the copper is ineffective. It would
be economical and quite as efficient, therefore, to use
a thin tube of copper. This result had been previously
obtained by Maxwell, Rayleigh, and Heaviside. The
latter especially has done excellent mathematical work
on this problem, and his solutions are much the most
complete. Thomson, however, popularised the theory,
and, in his presidential address to the Institution of
Electrical Engineers in 1889, he gave it in a form
which could be readily grasped by engineers. This
address, which was entitled " Ether, Electricity, and
Ponderable Matter," discussed problems to which
he had given much thought, and it excited much
interest.

In 1884 Thomson read to the Glasgow Philosophical
SocietjT- a paper on galvanometers for measuring potential
differences and currents. He also describes a regulator
he had devised for maintaining constant the electric
pressure applied to the lamps in his o^vn house. This
device was the forerunner of many similar ones for effect-
ing the same object.

A Httle later, in 1887, Thomson describes a " Double
Chain of Electrical Measuring Instruments, to measure
currents from the thousandth of an ampere up to 1000
amperes, and to measure pressures up to 40,000 volts."
In this paper he begins a description of the marvellous
series of voltmeters and ampere balances, with w^hich

84 LORD KELVIN

Ms name is insepara.bly associated. They are practi-
cally in universal use as standard instruments.

Thomson's earlier instruments were all made by Mr.
James White of Glasgow. He personally supervised
their construction, however, and was continually per-
fecting details in their design. He wanted his instru-
ments to be as useful in the test-room as in the laboratory.
He said that his ambition was that boxes leaving the
factory should be labelled " Glass — without care ; any
side up.". The making of Thomson's instruments soon
developed into quite a large industry. The business is
now owned by a private company, under the title of
Messrs. Kelvin & James White, Ltd. They have
large works in Cambridge Street, Glasgow.

In 1889, with the help of some of his students, he
made a determination of the number of electrostatic
units of potential in the electro-magnetic unit of potential,
and obtained a result the inaccuracy of which was less
than the half of one per cent. He also perfected methods
of standardising ampere balances by means of a copper
voltameter. One of his old pupils relates that Pro-
fessor Ayrton retested in London one of the balances
standardised in Glasgow. He found that the error of
the reading was about the tenth part of one per cent,
high. Thomson's jubilation was natural and justified
when he found that practically the whole error could
be attributed to the difference between the force of
gravity in Glasgow and London.

In 1891 Thomson gave an interesting and suggestive
lecture to the Royal Institution on " Electric and
Magnetic Screening." The importance of electrostatic
screening in electric theory is not sufficiently recognised.
Green was the first to give a rigorous proof that a
continuous metallic surface acts as a perfect screen
against all electrostatic influence. Faraday gave an

ELECTRICAL ENGINEER 85

elaborate experimental demonstration of the truth of
this. The lecturer showed many experiments illus-
trating partial screening by sheets of metal, and showed
how the results might have been predicted by the method
of images. A screen of imperfectly conducting material
acts as efficiently as a screen of metal, if sufficient time
be allowed. But when the electrostatic force varies
rapidly, the efficiency of the screening is much less.
On a damp day a sheet of paper will sometimes
act almost like a perfect screen. The screening effect
is increased by blackening the paper with ink on both
sides.

To screen off magnetic action is very much more
difficult than to screen off electric action. Even with
the best magnetic iron only partial screening can be
obtained. The best screen is obtained by surrounding
the space by a thick shell of iron. The conning-tower
of a battleship screens off a large fraction of the earth's
magnetic field from a compass placed inside it. Measure-
ments prove that a conning-tower, having a belt of iron
one foot thick, five feet high, and ten feet in internal
diameter, screens off 80 per cent, of terrestrial magnetism
from a compass placed at the centre of the belt.

Kelvin was a strong advocate of the continuous
current system of electric lighting. A few months
before his death, he spoke in the discussion on a paper
on the Thury high-tension continuous current system,
read by Mr. Highfield to the Institution of Electrical
Engineers. Notwithstanding the improvements which
have been made in polyphase methods of distributing
power — improvements which no one appreciated more
than himself — he said, " I have never sv/erved from the
opinion that the right system for long-distance trans-
mission of power by electricity is the direct current
system."

86 LORD KELVIN

He related how, many years ago, Lord Rayleigh had
said to him that he was glad that alternating currents
were being used in practice, as people will now learn
the subtleties of electrical science, a knowledge of which
was unnecessary so long as they use continuous current.
Rayleigh also prophesied that engineers would ulti-
mately come back to the use of the latter. The first
part of the prophecy has been fulfilled. For twenty
years technical schools have given youthful engineers a
thorough grounding in the " subtleties " of electrical
science. It seems probable that Mr. Highfield's paper
foreshadows the return to continuous current.

CHAPTER XI

CONCLUSION

Lord Kelvin was twice married. In 1852 he married
Miss Crum, daughter of Walter Crum, E.R.S., who was
a first cousin of Thomson's father. She died in 1870.
During a visit to Madeira in 1873, when acting as con-
sulting engineer for the Western and Brazilian Cable
Company, he met Miss Blandy, daughter of C. R.
Blandy, of Madeira, whom he married in 1874.

In 1860 Thomson had a serious accident when curling.
He sHpped on the ice, and, falling heavily, had the great
misfortune to fracture the neck of his thigh-bone. This
rendered him permanently lame. During the months
when the hmb was in splints, although he sometimes
suffered great pain, yet his mind was always occupied
with physical problems. His pencil and his note-book
were his inseparable companions.

During the last years of his Hfe his general health was
good, but he was afflicted with a very severe form of

CONCLUSION 87

facial neuralgia, which proved very intractable to treat-
ment. He endured the paroxypsms with great fortitude
and patience, and immediately they were over he re-
commenced liis work.

During the autumn of 1907 Lady Kelvin had a serious
illness. On November 23 Lord Kelvin caught a chiU.
This, superposed on his natural anxiety about Lady
Kelvin, confined him to his bed. He stiU for a week
or two struggled on doing some work, but gradually he
became weaker, and died on December 18.

On December 23 he was buried in Westminster Abbey
with all the honours due to a prince of science. The
service was simple and impressive, and the prominent
note was that of thanksgiving. The mourners, whilst
lamenting the loss of their beloved and revered master,
yet rejoiced that it had been given to him to set for aU
time an example of a noble, unsuUied, and strenuous life
spent in the arts of peace, and crowned with such a
noble record of work done for the benefit of humanity.

It is satisfactory to remember that many tributes
in- appreciation of his labours were paid to him in his
lifetime. When President of the Royal Society, in 1892,
Queen Victoria raised him to the Peerage, %\dth the title
of Baron Kelvin of NetherhaU, Largs, Later on King
Edward elected him into the Order of Merit, when that
order was first instituted. Both Germany and France
bestowed the highest dignities on him. A hst of the
honorary degrees conferred on him by universities and
of the honorary memberships of scientific societies to
which he was elected would fill several pages.

In the bibliography pubhshed in the Life of Lord
Kelvin, by Silvanus Thompson, the titles of 661 of his
papers are given. His Reprint of Papers in Electricity
and Magnetism, published in 1872, is still one of the
classical treatises on the subject. The influence of this

88 LORD KELVIN

work can be perceived in every modern book on elec-
tricity. His articles in Nichols^ Eficyclopcedia, in the
Encyclopcedia Britannica, and in various magazines are
well known, and have often been republished. His
Popular Lectures and Addresses are published in three
volumes. The first is on the Constitution of Matter,
the second is on Geology and General Physics, and the
third is on Navigation. His Mathematical and Physical
Papers have been published in six volumes, the last
three of which have been ably edited by Sir Joseph
Larmor. During the concluding years of his life he
derived much pleasure from rewriting and carefully
editing the Baltimore Lectures, which he delivered to
the Johns Hopkins University in 1884.

The above brief sketch of the hfe of a man of genius
shows what a quantity of glorious work can be crowded
into one man's lifetime. The childhood in Ireland ; the
busy and happy years as a boy student at Glasgow
University, coloured by dreams of the discoveries he
would make in unravelling Nature's mysteries once he
had acquired the requisite skill with the mathematical
tools. The active and strenuous Hfe at Cambridge when
he was preparing himself for Hfe's work, and where
he first proved that he could wield the philosopher's
tools with masterly skill. The full and varied hfe at
Glasgow University, brightened with the discoveries
that were then opening up a new page on the scroll
of science. His enthusiasm for the submarine cable,
which was to link the nations together in the cause of
peace. The dawning of an electrical age, which would
render antiquated the " marvellous scientific inven-
tions " of his boyhood. The busy life of a consulting
engineer, with, its struggles and successes. The Presi-
dentship of the Royal Society, with the multifarious
duties which it entails. His professorial jubilee, when

CONCLUSION 89

delegates came from every part of the world — ^from
kings, from learned societies, and from colleges — all
vjdng to do him honour. The enthusiasm with which
he was claimed by scientists as their leader marks an
epoch in the history of the world.

Although he derived substantial material benefits
from his labours, yet where science was concerned he
gave both time and money freely. The making of his
electrical instruments and of his compass and sounding-
macliine created a small but flourishing industry. But
the perfecting of apparatus for demonstration or re-
search purposes, the making of tide-predicting machines
and of machines for solving equations were labours of
love. The following story throws a hght on his manner
of attacking problems. When carrying out experiments
on the spectra of liquids at. Glasgow, the writer once
heard his assistant, M'Farlane, tell him that the hollow
prism which had come from White's was not properly
made. Thomson at once told him to send it back to
be remade. " If they cannot do it, send it to London,
and if no one there can do it, send it to Paris. I must
have a proper prism." Amongst the large number of
scientific men who developed some of Kelvin's ideas,
and delighted to acknowledge their indebtedness to
him, the following may be specially mentioned : Helm-
holtz, Clerk Maxwell, Stokes, Mascart, Sir George Dar-
win, Sir Charles Niven, Sir Alfred Ewing, and Professor
Chrystal. Among his pupils, Professors Jack, Ayrton,
Perry, Andrew Gray, Gibson, and Carslaw may be
mentioned. Professor A. Gray, Kelvin's successor at
Glasgow University, has written an excellent biography
of him. Professor Carslaw has written a standard work
on Fourier's Series. Amongst the younger generation
there are several electrical engineers, as, for example,
Professors Cormack, W. Buchanan, and J. B. Hender-

90 LORD KELVIN

son. But only a small fraction of Kelvin's students
followed on his own lines. The great bulk of them were
studying for professional or commercial careers. Some
of them have become judges, bishops, generals, consulting
physicians, and engineers. One is Sir William Ramsay,
the great chemist, and another is the Archbishop of
York. We must also specially mention the large number
of Japanese students who studied under him, and now
hold leading posts in their own country. All old students
look back on their attendance at Kelvin's lectures as
something never to be forgotten and to be treasured
deep in their hearts.

The advice Kelvin gave to his old students when
starting on their careers was of great value to them.
He also often gave them letters of introduction, which
they found of the greatest service. The letters were
generally typewritten, but occasionally he sent holo-
graph letters. At the time of Lady Kelvin's illness,
and only a fortnight before he himself was incapaci-
tated by his last illness. Lord Kelvin wrote the author
the letter shown on the opposite page, regretting his
inabihty to be present at the reading of the author's
paper at the Institution of Electrical Engineers.

Whilst speaking of his own work. Lord Kelvin, Hke
Sir Isaac Newton, was impressed with the smallness of
that which had been actually achieved in comparison
with what had been attempted. For instance, in his
speech at his jubilee he said that, after fifty-five years
of constant study, he knew little more of electricity and
magnetism than he did at the beginning of his career.
He thus pointed out the boundless, unexplored fields
which still stretch in endless vista before the scientific
man. Macaulay said much the same when discussing
the Baconian method. " These are but a part of its
fruits and of its first-fruits. For it is a philosophy

CONCLUSION

91

which never rests, which has never attained, which is
never perfect. Its law is progress. A point which
yesterday was invisible is its goal to-day, and wiU be
its starting-post to-morrow."

NETHERHAUL.
LARGS.

AVPSMIRE.

V^^L^x^ u>-e^ M^^<>A

Kelvin had a powerful imagination, a strong iB«
ductive faculty, and a power of realising his concept
tions in practice, which has only been equalled by the
greatest inventors. The possession of three such
faculties by the same man is probably unique. His
deductions were not of such world-wide importance as

92 LORD KELVIN

those of Isaac Ne^vton. It is very difficult to make a
comparison between these two intellectual giants, as
the ages in which they Hved are so far apart. Newton
was more painstaking and thorough. He pubhshed
little that was open to criticism. Kelvin, on the other
hand, could hardly wait until his experiments were
finished. There was so much to do and such a short
time to do it in. Whatever his hand found to do he
did with all his might, and the world knew the result. If
it was not satisfactory, then he would reshape and re-
polish it. He welcomed co-operation in his work. In
his senior class he often attacked original problems on
the board, and invited his students to help him in work-
ing out details.

His work Hves, and wlU continue to Hve. To him it
has been given to make history, which will hve so long
as intelhgent man survives on this earth. As the years
roll on, our indebtedness to him increases. May his
memory long be kept green in the land he loved so well.

REFERENCES

Popular Lectures and Addresses. By Sir William Thomson.
Vol. I, Constitution of Matter.
Vol. II. Geology and General Physics.
Vol. III. Navigation.

Reprint of Papers on Electrostatics and Magnetism. By Sir
William Thomson.

Treatise on Natural Philosojjhy. By Sir William Thomson
and Professor P. G. Tait. Vol. I., Parts I. and II.

Elements of Natural Philosophy. By Sir William Thomson
and Professor P, G. Tait. Part I.

Mathematical and Physical Papers. By Lord Kelvin. Vols. I.
to VI.

Baltimore Lectures on Molecular Dynamics and the Wave Tlieory
of Light. By Lord Kelvin.

Lord Kelvinh Early Home. By Elizabeth King and Elizabeth
Thomson King.

The Life of William Thomso7i, Baron Kelvin of Largs. By
SiLVANus P. Thompson. Vols. I. and II.

Lord Kelvin; an Account of his Scientific Life and Work. By
Andrew Gray.

H. von Helmholtz. By L. Koenigsberger. Translated hj F.
A. Welby.

The Life-Story of Sir Charles Tilston Bright. By C. Bright.

The Story of the Atlantic CaUe. By C. Bright.

For Biographies of the Scientists mentioned, see Tlie Dictionary
of National Biography.

Printed by Ballantyne, Hanson &^ Co.

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